In this work, we proposed a novel method, called Local Modified Zernike Moment per unit Mass (LMZMPM), for face recognition, which is invariant to illumination, scaling, noise, in-plane rotation, and translation, along with other orthogonal and inherent properties of the Zernike Moments (ZMs). The proposed LMZMPM is computed for each pixel in a neighborhood of size 3 x 3, and then considers the complex tuple that contains both the phase and magnitude coefficients of LMZMPM as the extracted features. As it contains both the phase and the magnitude components of the complex feature, it has more information about the image and thus preserves both the edge and structural information. We also propose a hybrid similarity measure, combining the Jaccard Similarity with the L1 distance, and applied to the extracted feature set for classification. The feasibility of the proposed LMZMPM technique on varying illumination has been evaluated on the CMU-PIE and the extended Yale B databases with an average Rank-1 Recognition (R1R) accuracy of 99.8% and 98.66% respectively. To assess the reliability of the method with variations in noise, rotation, scaling, and translation, we evaluate it on the AR database and obtain an average R1R higher than that of recent state-of-the-art methods. The proposed method shows a very high recognition rate on Heterogeneous Face Recognition as well, with 100% on CUFS, and 98.80% on CASIA-HFB.