Process for the polymerisation, preferably the gas phase polymerisation, of at least one alpha olefin containing from 2 to 12 carbon atoms in the presence of a supported chromium oxide based catalyst characterised in that - the supported chromium oxide based catalyst is a titanium modified supported chromium oxide based catalyst; - the chromium oxide based catalyst is supported on a refractory oxide; and - the titanium modified supported chromium oxide based catalyst has been subjected to a 2 steps thermal treatment wherein ∘ the first step consists in bringing the catalyst under an inert atmosphere to a temperature comprised between 600 and 900°C and then keeping the catalyst during a holding time of less than or equal to 8 hours under an inert atmosphere at a temperature comprised between 600 and 900°C, and ∘ the second step consists in the treatment of the catalyst coming from step 1 under an oxidizing atmosphere, preferably air, at a temperature comprised between 400 and 700°C during a holding time comprised between 2 and 10 hours, and ∘ wherein the maximum temperature of step 2 is always lower than the maximum temperature of step 1 and wherein the difference between the maximum temperature of step 1 and the maximum temperature of step 2 is comprised between 50 and 250°C, and further wherein the preparation of the catalyst is not carried out by the cogel method and involves the introduction of a titanium compound on to a support by addition and/or impregnation. - the supported chromium oxide based catalyst is a titanium modified supported chromium oxide based catalyst; - the chromium oxide based catalyst is supported on a refractory oxide; and - the titanium modified supported chromium oxide based catalyst has been subjected to a 2 steps thermal treatment wherein ∘ the first step consists in bringing the catalyst under an inert atmosphere to a temperature comprised between 600 and 900°C and then keeping the catalyst during a holding time of less than or equal to 8 hours under an inert atmosphere at a temperature comprised between 600 and 900°C, and ∘ the second step consists in the treatment of the catalyst coming from step 1 under an oxidizing atmosphere, preferably air, at a temperature comprised between 400 and 700°C during a holding time comprised between 2 and 10 hours, and ∘ wherein the maximum temperature of step 2 is always lower than the maximum temperature of step 1 and wherein the difference between the maximum temperature of step 1 and the maximum temperature of step 2 is comprised between 50 and 250°C, ∘ the first step consists in bringing the catalyst under an inert atmosphere to a temperature comprised between 600 and 900°C and then keeping the catalyst during a holding time of less than or equal to 8 hours under an inert atmosphere at a temperature comprised between 600 and 900°C, and ∘ the second step consists in the treatment of the catalyst coming from step 1 under an oxidizing atmosphere, preferably air, at a temperature comprised between 400 and 700°C during a holding time comprised between 2 and 10 hours, and ∘ wherein the maximum temperature of step 2 is always lower than the maximum temperature of step 1 and wherein the difference between the maximum temperature of step 1 and the maximum temperature of step 2 is comprised between 50 and 250°C,