A new tetranuclear cobalt(II) molecular square in which adjacent Co-II centers are linked by a mu(2)-bridging oxygen atom and a N-N bridge along the edges of the square has been designed for single-molecule magnets (SMMs) with high anisotropy barriers. The overall intramolecular ferromagnetic coupling at low temperature combined with the slow relaxation at static zero fields suggests a SMM behavior for this molecular square. The zero-field cooled magnetization (ZFCM) and field cooling magnetization (FCM) at 10 Oe illustrate the nonreversibility and bifurcation below 4.5 K. The deviations of magnetization from the saturated value in strong applied fields demonstrate the participation of low-lying excited states. The peaks of the out-of-phase signals are observed corresponding to coincidence of the applied ac field oscillation frequency with the relaxation rate.