Iterative methods for approximating the solution of a linear algebraic system \(Ax=b\) are considered. A multisplitting of the matrix A is a sequence of splittings of the form \(A=B-C\), where B is nonsingular. When coupled with weighting diagonal matrices one can form a parallel algorithm. Convergence results for different variants of the presented algorithm are given including a discussion of preconditioners for the conjugate gradient method. Numerical experiments indicate speedups (relative to computations done with one CPU or CE and with no vectorization) of about ten for the SOR multisplitting method, and six for the SSOR multisplitting preconditioned conjugate gradient method.