The bearing rings 1 and 2 of a rolling bearing is formed of one kind of
titanium alloys of .beta. type titanium alloys, near .beta. type titanium
alloys and .alpha.+.beta. type titanium alloys. The titanium alloy has a
surface hardness of Hv 400 or more and less than Hv 600 for increasing the
corrosion resistance and wear resistance of the bearing ring. Spherical
rolling elements 3 rolling on the raceway surfaces 1a and 2a of the
bearing rings 1 and 2 are formed of ceramics such as silicon nitride. When
.beta. type titanium alloys or .alpha.+.beta. type titanium alloys after a
solution treatment and applied with an oxidation treatment at a low
temperature of 400 to 600.degree. C. are used as the material for the
bearing ring, a bearing ring made of titanium alloy suitable to use under
a circumstance requiring corrosion resistance is obtained.