A fixed point theorem for a pair of random generalized non-linear contraction mappings involving four points of the space under consideration is proven. It is shown that this result includes the result of Lee and Padgett [1]. Also an application of the result is given. Key words : Complete probability measure space, d-algebras, Borel subsets, random operator, separable Banach space, upper semi-continuous functions. Bochner integral, Mathematics Subject classification: Primary 60H99, 47H10, and Secondary 60H 20
