A group of four aircraft was inbound to Brisbane on the same air route. Three of the aircraft were in close proximity with the lowest cruising at Flight Level(FL) 270 and the other two cruising at FL 350 and FL 370. The fourth aircraft was about 20 miles ahead cruising at FL 330. The aircraft cruising at FL 370, a Douglas DC-10, requested a clearance to descend when the aircraft was clear of traffic. The air traffic controller immediately cleared the aircraft to descend. The pilot did not respond to the transmission by the controller and the controller again cleared the aircraft to descend. The pilot advised the controller that there was another aircraft three miles ahead at FL 350. The controller apologised to the pilot and issued an instruction to the aircraft, a Boeing 737, cruising at FL 350 to turn right. The pilot of the aircraft at FL 370 then advised that he had the other aircraft in sight and that his aircraft had left FL 370 for FL 350. The controller immediately instructed the aircraft to maintain FL 370. Examination of the radar recording revealed that the higher aircraft had descended to FL 368 before commencing a climb to FL 370. At that time the aircraft were laterally separated by between four and five miles. As a result there was an infringement of the required separation standard of either 2,000 feet vertical or five miles horizontal separation between the two aircraft. The controller who issued the descent instruction was a trainee air traffic controller under training for the issue of her initial sector rating. At the time of the occurrence she was being supervised by a rated controller. The rated controller had instructed the trainee to issue the descent instruction to the aircraft and advised that he believed that when doing so the aircraft at FL 350 was in fact at FL 330. He was unaware why he had made that assumption as the altitude of the aircraft was correctly labelled by use of a 'shrimp boat'.