In this paper we propose a new fast algorithm of moment invariants computation, which needs almost no multiplications. We use modular arithmetic of finite Galois field GF(Q) to map geometrical moments calculation to a fast Fourier-Mellin-Galois transform, which reduces the computational complexity of moments from O(N 4 ) to O(N 2 log 2 N): We introduce orthogonal Fourier-Mellin-Galois moments based on a complete set of orthogonal characters of the multiplicative group of the GF(Q). These moments are modular remainders modulo Q of the classical geometrical moments.