An algorithm for computing inbreeding coefficients in large populations is presented. It is especially useful in large populations because of the small size of the memory required, which is linear with population size, and its speed, if the number of generations involved is not too large, ie not larger than about 12. The method is compared with 2 other methods for computational speed and memory requirement. The presented algorithm is suited for situations where the inbreeding coefficients for a few new animals are to be computed given that their ancestor's inbreeding coefficients were calculated previously.