In this paper, it is shown that Local Zernike Moments which is used in object and face recognition applications succesfully, can also used for face-pair matching problem. In this study, instead of using feature vectors produced by LZM directly, we focussed on reducing the dimensions of feature vectors and increasing the performance. In the light of experimental results, a new method called L2ML-YZM which depends on L2-Norm metric learning is suggested to make the feature vectors more discriminative. In L2ML space not only the dimensions of feature vectors are reduced, but also performance rate is increased 6% approximately. The comparison of performances between suggested method and other methods on Labeled Faces In The Wild (LFW) database has done and it is observed that suggested method has succesful success rate.