An outer ring 2 as a stationary ring is fabricated with a steel material having the composition as shown under. The steel material contains, as alloying elements, C 0.80 to 1.10 wt %, Si 0.20 to 0.50 wt %, Mn 0.2 to 1.0 wt %. It also contains any two kinds or more of Cr, Mo and V at rates of Cr: 1.2 to 3.5 wt %, Mo: 0.5 to 1.5 wt % and V: 0.2 to 1.0 wt %. The containing rates of Cr, Mo and V satisfy the under mentioned formula (1). It further contains Ti and/or Cu at rates of Ti: 0.05 to 0.20 wt % and Cu: 0.2 to 2.0 wt % 1.8≦[Cr]×0.6+[Mo]×0.5+[V]≦3.0  (1). Accordingly, it is possible to remarkably lengthen the life of a rolling bearing such as a bearing for alternator to be used under high vibration and high load.