The problem of approximation by polynomials with restricted coefficients, is considered in several papers (e.g. [7--9]). In [1--6], I have proved among other things, that every $f\i C_{[0,1]}$ can be approximated uniformly by a polynomial sequence $(P_n)_n$ such that $(P_n)_n$ is monotonically decreasing on $[0,1]$. The aim of this paper is to extend the ideas of [1--6] to the case of approximation by polynomials with restricted coeficients.