Process for preparing a supported catalyst for the polymerization and/or copolymerization of olefins which has a chromium content of from 0.01 to 5% by weight, based on the element, which comprises (a) preparing a homogeneous solution comprising an organic or inorganic chromium compound and at least one further organic or inorganic compound of elements selected from among Mg, Ca, Sr, B, Al, Si, P, Bi, Sc, V, Mn, Fe, Co, Ni, Cu, Zn, Zr, Nb, Mo, Ru, Rh, Pd, Hf, Ta, W in a protic or aprotic polar solvent, (b) bringing the solution from a) into contact with a finely divided inorganic support to form a catalyst precursor, (c) if appropriate, removing the solvent from the catalyst precursor and (d) calcining the catalyst precursor at temperatures of from 350 to 950° C., preferably 400 to 900° C., under oxidative conditions.