The processes that bring about the change of cell size in the evolution of salt‐finger convection are investigated with a numerical model of the convection in a Hele–Shaw cell. It is shown that the increase of cell width during the convection is produced by the vertical penetration of increasingly wider cells from the edges of the finger zone into the interior, as has been observed in a laboratory experiment. The increase of scale is also shown to occur through the merging process in which narrow finger cells merge to form wider cells. Occasionally, transition from wide to narrow scale can occur, in which case the wide finger cell splits to form two or more narrow cells. The scale transition produced by the merging, penetration, and splitting processes is shown to have the effect of maximizing the buoyancy flux generation in an evolving finger convection. This maximization is also interpreted in terms of the most rapidly growing finger mode. The effect of the scale transition on the actual magnitude of the buoyancy flux is related to the energy dissipation of fingers.