The invention relates to a condensation heat exchanger which comprises: —at least two concentric bundles (5, 5′) of tubes made from a material that is a good thermal conductor, inside which tubes a heat-transfer fluid is intended to circulate, each bundle of tubes (5, 5′) comprising a series of tubes (50, 50′) in the form of an arc of a circle, the tubes of each bundle (5, 5′) being arranged in parallel planes with a gap (53, 53′) between two adjacent tubes (50, 50′), —a single collector (6) made of a material that is a good conductor of heat and to which the two ends (51, 51′, 52, 52′) of each tube (50, 50′) of the various bundles (5, 5′) are connected, this collector (6) being equipped with inlet (61) and outlet (62) couplings. This exchanger is notable in that the collector (6) comprises several partitions delimiting various channels, which allow the fluid that is to be warmed up to be made to circulate in the various successive bundles from the outermost bundle to the innermost bundle.