In this paper, a method for triangulation of planar regions presented by MeLain in 1976 is briefly intrbduced. Then. this method is proved to be optimal in the sense that the minimum inner-angle of trlanglllated triangles is maximum, and the resultant triangnlation-is unique in the special ease. The proof is simple and elementary. but the result is quite attractive. McLain's algorithm can be effectively applied to computer graphies and finite element analysis.