Since G = L(3,2)SL(3.2), the elements in L(3,2) can be represented as third-order matrices on GF(2). Using fundamental group theory and matrix methods, the GF(3) module decomposition of the group L(2,2) is discussed, and in particular, the decomposability of the GF(3) module of L(2,2) is studied. It is considered that the GF(3) module of L(2,2) can be decomposed into the direct sum of irreducible modes, if V is the extraordinary mode of G and t∈G, o(t)=2 can make V/Cv(t)=2, then V=V1V0, where V1 is the G natural mode and V0=CV(G); If V/CV(G) is a G natural module, then V = V0, where G is irreducible and /C(G) is a G natural module, and | C(G)|≤2,V0≤CV(G