the present invention is directed to a novel halosilane cocatalyst component which may be used in conjunction with an aluminum - containing cocatalyst to provide enhanced catalytic activity of a vanadium based solid catalyst component in the polymerization of α - olefins . in addition to the enhancement in the catalytic activity obtaining using the present catalyst system , the resultant polymer produced by the present invention exhibits improved physical properties compared with polymers produced by prior art vanadium based catalyst systems . thus , the catalyst system of the instant invention represents an advance in the art in view of the combination of increased catalytic activity , i . e . yield of polymer produced , and enhanced physical properties of the polyolefin produced . in accordance with the present invention , a catalyst system is provided which comprises a solid catalyst component and a halosilane cocatalyst component . the solid catalyst component of the present invention is the product formed by admixing a solid inorganic oxide , an organometallic compound , a vanadium - containing compound and an organic reagent . in another aspect of the present invention , a process of the polymerization of α - olefins is disclosed . in this process at least one olefin is polymerized under olefin polymerization catalyst utilizing the catalyst system of the present invention , which includes the solid catalyst component of the present invention , and a cocatalyst selected from the group consisting of halosilane compounds and admixtures thereof with aluminum compounds .