A structure of at least a stationary-side race of a bearing is transformed into a lower bainite structure through an isothermal transformation treatment. Furthermore, the adjustment is made for hardness to HRC=54 to 64, an amount of residual austenite to not more than 5% and an area percentage of 0.8 .mu.m or longer carbide to not more than 20% based on the total area of secondary carbide. Thus is prevented the occurrence of a white layer in the rolling bearing.