Two one-dimensional cyano-bridged coordination polymers, namely, {[Mn-II(dapsc)][Mn-III(CN)(6)][K(H2O)(2.75)(MeOH)(0.5)]}(n)center dot 0.5n(H2O) (I) and I[Mn-II(dapsc)][Mn-III(CN)(6)][K(H2O)(2)(MeOH)(2)]}(n) (II), based on alternating high-spin Mn-II(dapsc) (dapsc = 2,6-diacetylpyridine bis(semicarbazone)) complexes and low-spin orbitally degenerate hexacyanomanganate(III) complexes were synthesized and characterized structurally and magnetically. Static and dynamic magnetic measurements reveal a single-chain magnet (SCM) behavior of I with an energy barrier of U-eff approximate to 40 K. Magnetic properties of I are analyzed in detail in terms of a microscopic theory. It is shown that compound I refers to a peculiar case of SCM that does not fall into the usual Ising and Heisenberg limits due to unconventional character of the Mn-III-CN-Mn-II spin coupling resulting from a nonmagnetic singlet ground state of orbitally degenerate complexes [Mn-III(CN)(6)](3-). The prospects of [Mn-III(CN)(6)](3-) complex as magnetically anisotropic molecular building block for engineering molecular magnets are critically analyzed.