The correlated function expansion (CFE) methodology has been used to estimate the energy band gay and the alloy bond length of Zn1-xMgxSeyTe1-y over the entire composition space (x, y). The lattice matching condition was obtained by optimizing the alloy bond length to the bond length of the substrates (ZnTe, InAs and InP), and the corresponding band gap and its bowing effect were identified. Excellent agreement was obtained between the CFE-estimated band gap and the recent photoluminescence data for the alloy grows on ZnTe and GaAs. As the CFE only requires ternary input data, it can accelerate efforts to find desirable quaternary alloy compositions.