Exchange biasing of diluted ferromagnetic alloys (low-TC weak ferromagnets) is a serious problem since basic condition TC>TN (TC and TN are Curie and Neel temperatures of a ferromagnet and antiferromagnet, respectively), fulfilled in conventional room-temperature spin-valves, is violated. The ability to exchange bias diluted ferromagnetic alloys is a keypoint for every kind of cryogenic spin-valve, Josephson or proximity, if low-TC alloy is utilized as a functional material in a superconductor-ferromagnet heterostructure. We present our recent finding of strong exchange biasing of Cu41Ni59 weak ferromagnet by CoOx/Cu41Ni59 interface with the aid of very thin cobalt sublayer adjacent to the CoOx antiferromagnet from the opposite side to the alloy layer. The magnetic properties of Si(substr.)/Si(buffer)/Co/CoOx/Cu41Ni59/Nb/Cu41Ni59/Si(cap) superconducting spin-valve system are investigated by SQUID magnetometry, and two strongly exchange biased signals are observed. The obtained results are compared with predictions of the domain state and spin-glass models of exchange bias.