Jungck [1] obtained a fixed-point theorem for a pair of continuous selfmappings on a complete metric space. Recently, Barada K. Ray [2] extended the theorem of Jungck [1] for three self-mappings on a complete metric space. In the present paper we omit the continuity of the mapping used by Ray [2] and replace his four conditions by a single condition. Our results so obtained generalize and/or unify fixed-point theorems of Jungck [1], Ray [2], Rhoades [3], Ciric [4], Pal and Maiti [5], and Sharma and Yuel [6].