In this paper, we propose a novel low-complexity separable but true 2D Hidden Markov Model (HMM) and its application to the problem of Face Recognition (FR). The proposed model builds on an assumption of conditional independence in the relationship between adjacent blocks. This allows the state transition to be separated into vertical and horizontal state transitions. This separation of state transitions brings the complexity of the hidden layer of the proposed model from the order of (N3T) to the order of (2N2T), where N is the number of the states in the model and T is the total number of observation blocks in the image. The system performance is studied and the impact of key model parameters, i.e., the number of states and of kernels of the state probability density function, is highlighted. The system is tested on the facial database of AT&T Laboratories Cambridge and the more complex facial database of the Georgia Institute of Technology where recognition rates up to 100 percent and 92.8 percent have been achieved, respectively, with relatively low complexity.