Abstract: The invention relates to a cooling system for a gas turbine. The cooling system according the invention comprises an annular array of turbine blades which comprises an undercut (17) formed in a blade platform (11). A substantially cylindrical damper pin (22) is arranged between two turbine blades (10a and 10b). The damper pin (22) comprises a cut-out (23) which is constructed and arranged that at least a portion of a gas flow which generally flows from a blade root portion to a blade profile portion of the turbine blades is directed to the named undercut (17). Since the named gas flow has a lower temperature than the blade platform and especially than the undercut, a cooling of the undercut is performed by the gas flow.