[en] By a recent development of the maximum-entropy method (MEM) following Sakata and Sato Acta Cryst. (1990), A46, 263-270, electron- (or nuclear-) density distributions have been obtained for crystalline materials of simple structures from single-crystal or powder diffraction data. In order to obtain a ME density map, the ME equation is solved iteratively under the zeroth-order single-pixel approximation (ZSPA) starting from the uniform density. The purpose of this paper is to examine the validity of the ZSPA by using a one-dimensional two-pixel model for which the exact solution can be analytically obtained. For this model, it is also possible to solve the ME equation numerically without ZSPA by the same iterative procedure as in the case of ZSPA. By comparison of these three solutions for a one-dimensional two-pixel model, it is found that the solutions obtained iteratively both with and without ZSPA always converge to the exact solution so long as the value of the Lagrange undetermined multiplier, λ, is chosen to be sufficiently small. This means the ZSPA solution does not depend on λ when the convergence is attained. When λ exceeds a critical value, iteration with ZSPA gives oscillatory divergence but iteration without ZSPA converges to a different value from the exact solution. It is concluded that the introduction of ZSPA does not cause any serious problem in the solution of the ME equation, when a sufficiently small λ value is used in the ME analysis. (orig.)