The aircraft departed from runway 16 at Melbourne and after becoming airborne the gear was retracted normally. A left turn was commenced at 500 feet which placed the aircraft on right base for runway 17 at nearby Essendon Airport. The gear selector was placed in the DOWN position as part of the pre-landing procedures but the aircraft subsequently landed with the gear retracted. Minor damage was sustained to the under-fuselage skin, gear doors and various aerials. Inspection revealed that the shear pin located in the forward door actuating linkage had failed. This pin is designed to shear if the doors attempt to operate out of sequence. The pre-impact rigging position of the doors could not be confirmed due to damage caused by the landing. The pilot reported that on short final he checked the gear lights, which were selected to dim. Because he failed to see the gear door warning light, which was the last and most conspicuous in the sequence, he assumed that he had a gear down indication.