Magnetism of any material depends on its crystal structure. However, two isostructural compounds such as MCuMoO₄(OH) (M = Na, K) can have markedly different magnetic properties. Herein, we introduce a new method to describe the linkages between the O-atoms and their bridged Cu²⁺ ions in order to clearly illustrate the structure–magnetic property relationships. This new method can account for magnetic differences between the two isostructural MCuMoO₄(OH) and is further confirmed by the rational design and development of a new compound KGaCu(PO₄)₂ with different linkages. The title compound crystalized in a space group of P2₁/c adopts a one-dimensional (1D) magnetically isolated S = 1/2 zigzag chain composed of elongated [CuO₆] octahedra via sharing alternately equatorial and skew edges. O atoms at the skew edges bridge the equatorial and axial orbitals of neighbouring Cu²⁺ ions (denoted EOA), while those at the equatorial edges bridge the equatorial orbitals of Cu²⁺ ions (EOE). The nearest-neighbour (NN) magnetic coupling of Cu²⁺ ions with the EOA linkage at 2.821 Å in the title compound is negligible, whereas the NN magnetic coupling of Cu²⁺ ions with the EOE linkage at 2.974 Å is essential. Therefore, the zigzag chain containing alternating spin-exchange dimers and no-spin-exchange ones is similar in electronic configuration to the dimerization of the quasi-one-dimensional antiferromagnet. Magnetic investigation of analogous compounds with a ‘trans–cis–trans–cis’ configuration observed in the title compound may shed light on structural evolutions associated with spin-Peierls (SP) transition.