At 0812, VH-CZL departed runway 16 at Melbourne on a 16 Cowes 5 departure with instructions to maintain 3000 ft. This departure involves tracking 170 deg until through 2500 ft or four miles DME and then tracking direct to Cowes which is on the Melbourne 150 deg VOR radial. After CZL made contact with departures control, the aircraft was cleared to climb to flight level 370. At 0813, N61CF departed from runway 17 at Essendon heading 170 deg and initially limited to 3000 ft. At 0815 CZL left 5000 ft and N61CF was cleared to climb to 4000 ft. Shortly afterwards N61CF was instructed "at 4000 ft turn right heading 260 deg". At 0816, N61CF was observed in a right turn and climbing through 4700 ft. At this time CZL was climbing through 5500 ft with N61CF less than two miles away and closing. N61CF was asked to confirm maintaining 4000 ft and passed traffic on CZL. The pilot of N61CF advised the traffic was in sight and apologised for the transgression.