a supported solid catalyst which can be used for the polymerization and copolymerization of conjugated dienes having as its basis the reaction product of : a ) a solid mgcl 2 support , b ) an ether , preferably thf , as swelling agent for the support , c ) a metal salt selected from among metals having an atomic number of between 57 and 71 or 92 in the periodic table of elements and , if the metal salt is not a halide , d ) a halogenation agent selected from the group consisting of a halogenated compound of aluminum and a halogenated compound not containing aluminum , the reaction solid being free from the swelling agent , plus e ) an organic derivative of aluminum which is obligatory when the halogenation agent is not a halogenated compound of aluminum and optional when the halogenation agent is a derivative of aluminum . also , a method of preparing this catalyst .