A supplementary crossover operator for genetic algorithms (GA) is proposed in the paper. It performs specific breeding between the two fittest parental chromosomes. The new child chromosome is based on the center of gravity (CoG) paradigm, taking into account both the parental weight (measured by their fitness) and their actual value. It is designed to be used in combination with other crossover and mutation operators (it applies to the best fitted two parental chromosomes only) both in binary and real-valued (evolutionary) GA. Analytical proof of its ability to improve the result is provided for the simplest case of one variable and when elitist selection strategy is used. The new operator is validated with a number of usually used numerical test functions as well as with a practical example of supply air temperature and flow rate scheduling in a hollow core ventilated slab thermal storage system. The tests indicate that it improves results (the speed of convergence as well as the final result) without significant increasing computational expenses. (c) Control and Cybernetics