Algorithms for computing various eigenvalues of the transport equation can be classified as direct and indirect. The latter computes the eigenvalue by an iterative search on another, generalized, eigenvalue. Direct computation is shown to be a special case of indirect computation. As a result of this analysis, a new “modified direct” algorithm was defined. The new algorithm also works in cases when the direct algorithm fails and it shows generally fast convergence. The proposed algorithm is applicable even to nonfissionable systems where the classical indirect approach via the k eigenvalue is possible only after an artificial “juggling” of cross sections.