The aircraft was being radar vectored for a right turn onto the ILS (Instrument Landing System) final. It was also on descent to the Radar Lowest Safe Altitude of 4,500 ft and was experiencing moderate turbulence. Just before levelling out at 4,500 ft, its GPWS (Ground Proximity Warning System) Alert activated and the crew immediately initiated a maximum performance climb, levelling at 6,000ft. Air Traffic Control was notified immediately. The aircraft was in cloud at the time of the occurrence. Investigation has revealed that the GPWS alert was a genuine warning occurring as the result of the aircraft's descent profile and the excessive closure rate to high terrain of Black Mountain which rises steeply from generally lower terrain to 3,493 ft above mean sea level. A previous incident involving a regular public transport service jet took place some three months earlier where the GPWS gave an alert whils the airacraft was approaching Black Mountain from the same westerly aspect. Air Traffic Services has raised the Radar Lowest Safe Altitude from 4,500 ft to 4,700 ft in the area of Black Mountain with the expectation that this will reduce the incidence of alerts.