In order to multiply matrices while minimizing the number of page fetches required, it is often more efficient to reorganize the data into submatrix form" and to use block multiplication rather than to use the best known algorithms which leave the matrices stored in row-(or column-) oriented form. An efficient method for accomplishing this reorganization is given. This also makes possible the derivation of an asymptotically better bound for multiplication of matrices given in row-· oriented form by adapting the technique of Strassen to the reorganized data. The reorganization/block multiplication scheme is shown to be advantageous for matrices and pages of realistic size; the Strassen adaptation is not. The former scheme is also shown to be advantageous even if the transpose of one of the matrices is available at no additional cost.