A simple linear identification algorithm is presented in this paper. The last principal component (LPC), the eigenvector corresponding to the smallest eigenvalue of a non-negative symmetric matrix, contains an optimal linear relation of the column vectors of the data matrix. This traditional, well-known principal component analysis is extended to the generalized last principal component analysis (GLPC). For processes with colored measurement noise or disturbances, consistency of the GLPC estimator is achieved without involving iteration or non-linear numerical optimization. The proposed algorithm is illustrated by a simulated example and application to a pilot-scale process. (C) 2000 Elsevier Science Ltd. All rights reserved.