A process for the manufacture of a titanium-containing component of a catalyst for the polymerization of monoolefins by the Ziegler-Natta method by milling (a) a titanium trichloride/aluminum trichloride complex and (b) a particular ether with one another, in which process (1) a vibratory ball mill producing a particular milling acceleration is used, (2) until from 6 to 85% of the aluminum trichloride originally present in a bonded form in the titanium-containing compound (a) have been eliminated from the said compound (a). Polyolefins of high stereoregularity can be obtained in a high specific yield by means of the catalyst component manufactured according to the invention.