Four dimensional Gallant-Lambert-Vanstone (GLV) method can be applied for faster scalar multiplication on some elliptic curves over F_p2 , such as the Longa-Sica GLS curves with special complex multiplication (CM), and the Guillevic-Ionica's curves via Weil restriction. This study generalizes Long-Sica four dimensional GLV decomposition methods, and gives explicit and efficient decompositions in quartic CM fields for such elliptic curves as well as the bound for the decomposed coefficients. The presented results well support the GLV method for faster implementations of scalar multiplications on desired curves.