The present invention relates to a process for the polymerization of a polyolefin, preferably polypropylene, in a polymerization reactor by contacting one or more olefins, preferably propylene, with a catalyst system in said reactor while stirring, said catalyst system comprising: * a procatalyst comprising 1) a magnesium-containing support, 2) titanium, 3) a phthalate-free internal electron donor; and 4) optionally an activator; wherein said procatalyst is obtained by the following process: i) contacting a compound R4, MgX42—, with an alkoxy- or aryloxy-containing silane compound to give a first intermediate reaction product, being a solid Mg(OR1)xX12-x, R4 is the same as R1 being a linear, branched or cyclic hydrocarbyl group independently selected from alkyl, alkenyl, aryl, aralkyl, alkoxycarbonyl or alkylaryl groups, and one or more combinations thereof; wherein said hydrocarbyl group may be substituted or unsubstituted, may contain one or more heteroatoms and preferably has between 1 and 20 carbon atoms; wherein X4 and X1 are each independently a halide; z is in a range of larger than 0 and smaller than 2, being 0