Inclusion criteria:

          -  Documented diagnosis of Myelodysplastic Syndromes (MDS) according to World Health
             Organization (WHO) criteria that meets International Prognostic Scoring System (IPSS)
             classification of low or intermediate-1 risk disease at screening as determined by
             microscopic and standard cytogenetic analyses of the bone marrow and peripheral
             complete blood count (CBC).

               -  Phase I dose escalation: patients who experienced Erythropoiesis-Stimulating
                  Agents (ESA) treatment failure or do not qualify (serum erythropoietin level >
                  500 U) for ESA treatment, and are refractory to or not amenable or eligible for
                  established MDS therapy (Hypomethylating Agents (HMA), lenalidomide)

               -  Phase I expansion:

                    -  Expansion cohort 1 ("pre-treated"): patients who experienced ESA treatment
                       failure or do not qualify (serum erythropoietin level > 500 U) for ESA
                       treatment and are refractory to established MDS therapy (HMA and /or
                       lenalidomide)

                    -  Expansion cohort 2 ("untreated"): patients who experienced ESA treatment
                       failure or do not qualify (serum erythropoietin level > 500 U) for ESA
                       treatment and who have not received prior HMA and/or lenalidomide (because
                       not amenable or eligible for these treatments).

               -  Phase II: patients who experienced ESA treatment failure or do not qualify (serum
                  erythropoietin level > 500 U) for ESA treatment. For definition of further
                  details of the phase II patients to be included the protocol will be amended
                  based on Phase I results

          -  Patient is non-responsive to, refractory to, or intolerant of ESAs, or ESAs are
             contraindicated or unavailable, or a documented serum erythropoietin level of > 500
             U/L.

          -  Eastern Cooperative Oncology Group (ECOG) Performance Status <=2.

          -  Age >= 18 years.

          -  Written informed consent which is consistent with International Conference on
             Harmonization - Good Clinical Practice (ICH-GCP) guidelines and local legislation.

        Exclusion criteria:

          -  Patient with IPSS category of Int-2 or high-risk MDS.

          -  Phase II only: Patients with a deletion 5q cytogenetic abnormality.

          -  Treatment within 28 days prior to Cycle 1 Day 1 with: i) long acting erythropoiesis
             stimulating agents, ii) long acting Granulocyte colony-stimulating factor (G-CSF),
             iii) granulocyte- macrophage colony stimulating factor (GM-CSF), iv) 5-aza,
             lenalidomide or decitabine, or v) iron chelation and within 14 days prior to Cycle 1
             Day 1 with short acting erythropoiesis stimulating agents and short acting G-CSF.

          -  Patient previously received allogeneic bone marrow or stem cell transplantation.

          -  Second malignancy currently requiring active therapy (except for hormonal/antihormonal
             treatment, e.g. in prostate or breast cancer).

          -  Aspartate amino transferase (AST) or alanine amino transferase (ALT) > 2.5 times the
             upper limit of normal (ULN).

          -  Bilirubin >1.5 mg/dL, except for Gilbert's Syndrome or hemolysis.

          -  Serum creatinine >2.0 mg/dL.

          -  Known human immunodeficiency virus (HIV) infection and/or active hepatitis B infection
             (defined as presence of Hep B DNA), active hepatitis C infection (defined as presence
             of Hep C RNA).

          -  Presence of concomitant intercurrent illness, or any condition which in the opinion of
             the Investigator, would compromise safe participation in the study, e.g. active severe
             infection, unstable angina pectoris, new onset of exacerbation of a cardiac
             arrhythmia.

          -  Psychiatric illness or social situation which in the opinion of the Investigator would
             limit compliance with trial requirements.

          -  Patient receiving concomitant therapy, which in the opinion of the Investigator is
             considered relevant for the evaluation of the efficacy or safety of the trial drug.

          -  Female patients of childbearing potential who are sexually active and unwilling to use
             a medically acceptable method of contraception during the trial and for 6 months after
             the last administration of BI 836858, i.e. combination of two forms of effective
             contraception (defined as hormonal contraception, intrauterine device, transdermal
             patch, implantable or injectable contraceptive, bilateral tubal ligation etc.).

        Women of childbearing potential are defined as females who:

          -  Have experienced menarche and

          -  Are not postmenopausal (12 months with no menses without an alternative medical cause)
             and

          -  Are not permanently sterilized (e.g. hysterectomy, bilateral oophorectomy or bilateral
             salpingectomy

               -  Male patients with partners of childbearing potential who are unwilling to use
                  condoms in combination with a second effective method of contraception (defined
                  as hormonal contraception, intrauterine device, condom with spermicide, etc.)
                  during the trial and for 6 months after the last administration of BI 836858.

               -  Pregnant or nursing female patients.

               -  Treatment with another investigational agent under the following conditions:

          -  Within two weeks (4 weeks for biologics) of first administration of BI 836858, or if
             the half-life of the previous product is known, within 5 times the half-life,
             whichever is longer.

          -  Patient has persistent toxicities from prior MDS therapies which are determined to be
             relevant by the Investigator.

          -  Concomitant treatment with another investigational agent while participating this
             trial.

               -  Chronic use, as defined by > 2 weeks of a corticosteroid agent that is >= 20
                  mg/day of prednisone or its equivalent, within 4 weeks prior to first
                  administration of BI 836858.

               -  Treatment with an immunomodulatory agent within 4 weeks prior to first
                  administration of BI 836858.

               -  Patient received prior treatment with a CD33 antibody.

               -  In the opinion of the Investigator patient is unable or unwilling to comply with
                  the protocol.

               -  Further exclusion criteria apply