A method for the production of dimethyl ether by catalytical reaction between carbon monoxide and hydrogen is disclosed, in which an improved catalyst system is used. The improved catalyst is composed of a mixture of oxides and/or salts of metals such as Al, Cr, La, Mn, Cu, Zn and their mixtures which have been subjected to a stabilization process with a compound of silicon having substituents of various natures; such as hydrocarbonaceous radicals, and halogens. This catalyst is a considerable advance over the prior art.