A film composed of grease, or a film composed of a thickener for grease, is formed on a portion of the surface of each of components constituting a bearing, the portion being opposed to a polymeric lubricant, whereby sliding frictional resistance between the bearing components and the polymeric lubricant is reduced. In the formation of the film, the assembled bearing in which the film has not yet been formed is immersed into a liquid which is obtained by diluting the grease or the thickener for grease with a solvent, and the solvent is then dried, thereby to highly reproducibly form the film of uniform thickness. In an assembled double-row self-aligning roller bearing wherein an outer race is swingable in a direction perpendicular to the center axis of the bearing, raw materials of a polymeric lubricant are poured into and solidified in two regions of an annular space between the inner and outer races.