The use of the Monte Carlo (MC) method for obtaining higher modes is an active area of current research. The method faces several difficulties in its implementation for practical problems. The study of simpler models in this context may be expected to provide insights into some of these problems. This technical note describes the development of a fission matrix algorithm based on the diffusion theory MC model to obtain fundamental and higher λ eigenvalues and eigenvectors (modes) of a reactor. A method for estimating variance in the estimated eigenvalues using first-order perturbation theory is also developed. The algorithm has been implemented in the space-time–kinetics MC code KINMC. The performance of the method for calculating higher eigenvalues and higher eigenvectors has been verified through comparison of the eigenvalues thus obtained with the results of other deterministic codes. Results of computation of eigenvalues and eigenvectors up to six modes are presented in this technical note.