Six tetranuclear Dy-III complexes [Dy-4(L)(2)(CH3OH)(3)(NO3)(3)]center dot 3NO(3)center dot 2H(2)O (1a), [Dy-4(L)(2)(CH3OH)(2)(SCN)(4)(OCH3)(2)]center dot 2CH(3)OH center dot 2H(2)O (1b), {[Dy-4(L)(2)(CH3OH)(SCN)(6)(CH3CN)]center dot 3CH(3)OH center dot 4CH(3)CN}(2) (2a), [Dy-4(L)(2)(CH3OH)(2)(SCN)(6)]center dot 6CH(3)OH center dot 2H(2)O (2b), [Dy-4(L)(2)(CH3OH)(2)(SCN)(4)(OCH3)(2)]center dot 5CH(3)OH center dot 2H(2)O (3a), and [Dy-4(L)(2)(CH3OH)(SCN)s(H2O)(2)]center dot SCN center dot 4CH(3)OH center dot 2H(2)O (3b) were structurally and magnetically characterized. The Dy1/Dy2 centers in these complexes are eight-coordinate and submitted to pseudo-D-4d symmetry environments. It is noteworthy that the modulation of coordination terminal around Dy1/Dy2 centers induces distinct magnetic relaxation processes, switching from single relaxation (1b) to two-step relaxation (2b). All complexes show significant zero-field single-molecule magnet (SMM) properties with the exception of 3b, which only features the slow magnetic relaxation behavior under a zero dc field. Ab initio calculations substantiate that the excellent SMM property of complex 1b should mainly profit from strong ferromagnetic interactions between the individual Dy-III ions, while different single-ion magnetism results in better SMM property of complex 3a than that of 3b.