A new comparison theorem is given for the nonlinear multisplitting relaxation method [1], and an important modification is proposed for it, too.

Lambert [1] proposed a one-step method based on Eulerʹs rule which effectively copes with ordinary differential equations. In the paper, he proved its stability for the equation of the type y′ = Ay, where A is a real symmetric matrix. We extend the concept and prove the stability when A is a real normal matrix.