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We report systematic first-principles calculations based on the full-potential linearized augmented plane wave method for 3 d transition-metal (V, Cr, Mn, Fe, Co, Ni) monolayers on the W (001) surface. We predict that V, Cr, and Mn monolayers exhibit a ferromagnetic ground state, while Fe and Co favor the c (2× 2) antiferromagnetic state. This trend is surprising as it is opposite to what was expected from the knowledge of magnetism in ultrathin films and results from strong hybridization at the W interface. In particular, this system is the first case showing antiferromagnetic Co.