Inclusion Criteria:

- Age ≥ 18 and < 66 years

- Patient with acute myeloid leukemia (AML) high risk in 1st complete remission:

- CR1 obtained by 2 cycles of chemotherapy,

- unfavorable Cytogenetics

- FLT3 Duplication,

- Or acute myeloid leukemia (AML) in 2nd complete remission,

- Or acute lymphoblastic leukemia (ALL) High-risk 1st complete remission:

- Presence of the translocation t (9; 22),

- Or acute lymphoblastic leukemia (ALL) in 2nd complete remission,

- Or Chronic Myeloid Leukemia (LCM) beyond the 1st chronic phase

- Or Myelodysplasia or with IPSS score with 2 or more

- Or Hodgkin's disease in sensitive relapse or beyond the 2nd complete remission. or
following types of lymphoma :

- Diffuse large B lymphoma cells relapsed or refractory after two lines of treatment or
after a line with autologous hematopoietic stem cell, or

- Mantle cell lymphoma relapsed or refractory after two lines of treatment or after a
line with autologous hematopoietic stem cell

- Others aggressive lymphoma for which an indication of allograft is selected (Burkitt
lymphoma, lymphoblastic lymphoma, intravascular lymphoma, ...)

- Lymphoma (low-grade follicular lymphoma, marginal zone lymphoma) in histological
transformation.

- Low-grade lymphoma for which an indication of allograft is retained

- Unable to receive myeloablative conditioning because of age (> 45 years) and/or the
existence of co-morbidities precluding a myeloablative conditioning (status ECOG > /
= 2, DLCO <50%, fungal infection proven or probable in the previous 60 days) and / or
prior treatment with total body irradiation at doses above 2 Gy or busulfan doses> 8
mg/kg

- No contra-indication for a transplant in allogeneic non-myeloablative conditioning,

- No HLA-identical sibling,

- Absence of an unrelated donor on national or international registering with a 10/10
allelic matching or a 9/10 allelic matching with the only tolerated mismatches
being: HLA-C.

- No unit of placental blood available fulfilling the characteristics of compatibility
(HLA compatible at least 4/6 allele or generic) and richness

- Provision of at least 2 units of placental blood, whose compatibility is 4/6, 5/6 or
6/6 and whose richness is before thawing, > 2 x 107 and < 3 to 4 x 107 nucleated
cells per/kg.

- Patient affiliated to a social security scheme,

- Free and informed consent signed by the patient and the investigator.

Exclusion Criteria:

- Age <18 and ≥ 66 years

- Malignant myeloid or lymphoid acute or chronic disease without indication for an
allogeneic transplant according to the criteria of European Bone Marrow
Transplantation Group.

- Able to receive a myeloablative conditioning because of age (<45 years) and the
absence of co morbidities (status ECOG> / = 2, DLCO <50%, fungal infection proven or
probable in 60 preceding days) and the absence of prior treatment with total body
irradiation at doses above 2 Gy or busulfan doses> 8 mg / kg

- Contra indication for a non-myeloablative conditioning,

- HLA-identical sibling available

- Availability of an unrelated donor on a national or international register with 10/10
or 9/10 HLA matching (HLA-C Mismatch tolerated).

- At least one unit of cord blood available with the characteristics of compatibility
(HLA compatible at least 4/6 allelic or generic) and richness (before thawing> / = 3
to 4 x 107 nucleated cells/kg recipient, by degree of compatibility)

- Absence of at least 2 units of placental blood, whose compatibility is 4/6, 5/6 / or
6/6 and whose richness before thawing is > 2 x 107 and < 4 x 107 nucleated cells
per/kg of recipient.

- Women of childbearing age not using contraception, pregnant or lactating