In this paper we introduce a new genetic algorithm for register allocation. A merge operator is used to generate new individual solutions. The number of steps required to examine all pairs in the population matrix to generate n2 (n is the population matrix size). Generating an offspring from the parents needs m steps (m number of nodes). The total number of steps required by the algorithm is n2m, that is, the genetic algorithm has a linear time complexity in terms of number of nodes. The experimental results show optimal solutions in many of the graphs used for testing.