The [Cu4OCl6(IMIDH)(4)] complex has been synthesized and its crystal structure and magnetic properties determined. The compound crystallizes as a dark green solid in the orthorhombic system, space group P2(1)2(1)2(1), With cell constants a = 11.469(2) Angstrom, b = 13.933(2) Angstrom, c = 16.778(3) Angstrom and four formula units per cell. The complex has a tetrameric structure of four copper(II) ions connected to a central oxo group, in an approximately tetrahedral arrangement. Copper coordination is completed by three mu(2)-chloride ions and an imidazole nitrogen atom, defining a trigonal bipyramidal environment around each copper ion. A new Heisenberg exchange scheme has been developed, considering the experimentally observed distortion of the Cu-4 tetrahedron. The magnetic susceptibilities measurements were interpreted by means of this model, in terms of three coupling constants, J = -7.65 cm(-1) J(s) = 83.3 cm(-1), and J(L) = -58.8 cm(-1), which show a linear correlation with the observed Cu-O-Cu angles.