The following convex program \[ \max \{\phi_ 0(x)=(c_ 0,x)| \phi_ 1(x)\geq 0;\quad (b_{\nu},x)\leq \beta_{\nu},\quad \nu =1,...,N\} \] where \(\phi_ 1(x)\) is a concave function and \(\Omega =\{x\in E^ n\) : \((b_{\nu},x)\leq \beta_{\nu}\), \(\nu =1,...,N\}\) is a bounded set. The proposed algorithm is a combination of the method of cutting planes and the method of Chebyshev centers and in a precise sense is related to the method of centered cuts. The value of this method is the convergence at the rate of a geometric progression and the possibility of eliminating at each step those inessential restrictions which are related to the preceding steps.