It is shown in this paper that by choosing suitable forms for 4×4 matrices as products of Dirac matrices and matrices of rank unity (i.e., products of 4×1 and 1×4 matrices), and expressing them as linear combinations of the sixteen elementsγ A of the basis of the Dirac algebra, one can derive the generalized identities of Pauli which hold in this algebra. Generalizations are given for cases not dealt with by Pauli, and the use of his B-matrix is also avoided. The same method yields further ‘tensor’, multilinear, and polynomial identities of which it is shown that the last two kinds of identities are derivable from bilinear and quadratic ones. It is pointed out that all types of identities can be deduced by considering five primitive types of matrices.