Linear discriminant analysis (LDA) is a basic tool of pattern recognition, and it is used in extensive fields, e.g. face identification. However, LDA is poor at adaptability since it is a batch type algorithm. To overcome this, new algorithms of online LDA are proposed in the present paper. In face identification task, it is experimentally shown that the new algorithms are about two times faster than the previously proposed algorithm in terms of the number of required examples, while the previous algorithm attains better final performance than the new algorithms after sufficient steps of learning. The meaning of new algorithms are also discussed theoretically, and they are suggested to be corresponding to combination of PCA and Mahalanobis distance.