The in‐plane uniaxial anisotropyKu, induced by a magnetic field applied during the deposition, was investigated in amorphous thin films of Co1−xZrxand Co1−x−yZrxMy(M=Ti, Nb, and Pt) obtained by rf sputtering. For a given concentrationKupresents a bell‐shaped variation as a function of Ar pressurePAr. The critical pressure for which the maximum value ofKuis obtained and the absolute value of (Ku)maxchanges for the various alloys. These results and the high value of (Ku)maxare explained by a model where (Ku)maxis related to the local anisotropy via the local structure upon the nonmagnetic metal. (Ku)minis essentially related to a pseudodipolar short‐range order.