Inbreeding coefficients of animals are required in many genetic analyses of livestock records. A modification of Colleau's indirect algorithm to compute inbreeding coefficients in large populations is presented. With overlapping generations, the modified algorithm evaluated all progeny of each sire simultaneously in one back and forth exploration of a reduced pedigree. Simulation for a relatively large number of generations, different number of sires, family sizes and mating designs showed that Colleau's algorithm was faster (from 1.2 to 143 times) than two other algorithms under comparison (Tier, modified Meuwissen and Luo), in all situations investigated. Modifying Colleau's algorithm considerably decreased computation time (from 50 to 89%), resulting in a very fast algorithm. The number of sires mostly affected computational efficiency of the modified algorithm, whereas family size and mating design had virtually no effect. In the updating situation, when only animals born in the last year were evaluated, given known inbreeding coefficients for the other, the modified algorithm was also fast compared with the other three algorithms. Memory requirements for the algorithms were also discussed.