In the literature very little is known about preconditioning the linea
r system for the successive overrelaxation (SOR) method. In this paper
we investigate how the convergence rate of the SOR method is affected
if the linear system is preconditioned by one Gauss-Jordan eliminatio
n. It is shown that under some conditions the SOR method applied to th
e preconditioned system gives improvement in the rate of convergence.