The instability of Fornberg’s pattern for leapfrog time integration of the nonlinear convective equation ∂u/∂t + u∂u/∂x = 0 is found to occur as a closed three-mode process and to include the sideband instability. The perturbation about Fornberg’s pattern is able to be unstable for both physical and computational modes. The growth rates as well as the excitation mode spectra of the perturbation are shown to agree with experimental results. © 1995 Academic Press, Inc.