The possibility of a ferrimagnetic-in-plane configuration with C(2X2) symmetry is analyzed for V, Cr and Mn monolayers deposited on Fe(001). The spin-polarized electronic distribution is calculated by solving self-consistently a tight-binding Hamiltonian in a mean field approximation. The relative stability of this solution with respect to the usual P(1X1) ferromagnetic-in-plane solution is determined by means of the difference of total energy. A nearly zero surface magnetization is obtained in the C(2X2) arrangement. The results of this study are discussed in relation with recent experimental observations.