Vector quantization (VQ) is a well-known signal compression method. The encoding process of VQ is extremely time-consuming so that it limits the practical applications of VQ method to a great extent. In order to speed up the process of VQ encoding, the previous works (J.Z.C. Lai, et al, IEEE Trans. Image Processing, Vol. 13, No. 12, pp.1554-1558, 2004; S.J. Baek, et al, Signal Processing, Vol.75, pp.89-92, 1999) have reported that the projection concept of a vector is very effective for rejecting most of unlikely candidate codewords to speed up VQ encoding process. In both of these two previous works, they used a set of three symmetric projection axes or generalized central axes like p 1=T, p2=[11111111-1-1-1-1-1- 1-1-1]T and p3=[11-1-111-1-111-1-111-1-1]T for rejection tests in the case of 4×4 block size. In addition, they reported that if and only if these three axes of (p1, p2, P 3) can experimentally guarantee the best search performance of VQ encoding. However, both of these two previous works did not give out the reasons to show why this set of (p1, p2, P3) axes is the best choice for projection axes. It is a remaining important problem in the two previous works. This paper aims at providing a verification and an explanation to the best choice of (p1, p2, p3) set and meanwhile proposing a criterion on how to choose the projection axes optimally based on the concept of Walsh transform. Experimental results confirmed the effectiveness of the proposed criterion.