The invention relates to antibodies to the tumor-associated antigen CD33 and to the use thereof for immunotargeting CD33-positive cells. The antibodies according to the invention are suitable for use in the field of medicine, pharmaceuticals, and biomedical research. According to the invention, the aim is achieved by means of novel anti-CD33 antibodies comprising the complementary determining regions (CDRs) defined in the claim. The antibodies according to the invention are characterized by a high affinity for human CD33, of the order of magnitude of 1010 mol/l. The CDR sequences according to the invention are suitable in particular for producing recombinant fragments (such as scFv fragments or bispecific antibodies) and for immunotargeting, due to the high affinity thereof. The invention further relates to the use of an antibody according to the invention for producing a medication for therapeutic and/or diagnostic application for illnesses associated with the expression of CD33, particularly for acute myeloid leukemia (AML). The invention thus also comprises a pharmaceutical composition comprising one or more antibodies according to the invention in association with a pharmaceutically acceptable thinning agent or carrier.