The size and the density of the collision probability matrix have been recognized as major deficiencies since the early era of development of the collision probability method. The computing time of the matrix inversion is proportional to the third degree of the number of unknowns per group and increases rapidly with the increase of the problem size. This is a severe limitation that restricts the capabilities of the method and makes it inapplicable to large-size neutron transport problems. This paper presents a new solution method that overcomes these deficiencies and extends the capabilities of the collision probability approximation. To reduce the matrix inversion time, a block partition is applied, and the solution is obtained by block iteration. Owing to the partition, the method is suitable for parallel calculations on contemporary computers. To illustrate the potential advantages, the following three groups of calculations are presented. In the first group, results of sequential calculations reveal the advantage over traditional methods of direct solution and point iteration. In the second group, memory shared parallelism results present the speedup that can be achieved in solving medium-size problems on a standard multicore desktop computer. In the third group, distributed memory calculations show an example of the solution of a large-size two-dimensional model problem of a heavy water power reactor invoking 100 thousand unknowns per group.