A variational method not restricted to a given class of trial functions is proposed for obtaining the electron density minimizing the energy functional E[n] directly in the surface region of jellium. Remaining within the local-density approximation, the kinetic-energy contribution is considered as proposed by Kirzhnits. Results are compared to those obtained by Lang for investigating the influence of the approximation used for the kinetic energy. The electron density minimizing the approximated energy functional E[n] does not show any oscillation; only one dominant peak appears at the edge of the jellium if ${r}_{s}$ is greater than 2.