The method for calculating the generalized first-flight collision probability in a lattice system with a certain total cross section by the exact generalized first-flight collision probability in a system of the same geometry, having a different standard total cross section, is presented. The time required to calculate the multigroup integral transport problem, can be reduced greatly using this approximation; a large part of the time is consumed by the numerical integral calculation of the collision probabilities in all the energy groups. It is proved that the approximate collision probabilities obtained satisfy the conditions, i.e., the neutron conservation and the reciprocity relation. It is also shown by numerical calculation that the zero'th approximation using the first-flight collision probability gives very good values in the isolated or latticed systems.