Abstract: A new algorithm with a structure containing two incremental principal component analysis (PCA) modules is proposed to solve the incremental linear discriminate analysis (LDA) problem. A residual covariance natural power (RCNP) PCA method and lossless update equations of both a within-class scatter matrix and a covariance matrix are also proposed for accelerating convergence of the incremental LDA. Simulation results show that the proposed method provides faster convergence, and better performance in complex computations and in ease of operation compared to other incremental LDAs.