During April 1944, No. 78 Wing received orders to move again, this time to support Operation Reckless, the American landing at Hollandia in western New Guinea. The main party of the squadron departed Cape Gloucester on 17 April bound for Tadji airstrip on the mainland of New Guinea, and its Kittyhawks arrived there on the 24th of the month. No. 78 Squadron began flying patrols over the American beachhead at Hollandia the next day. The squadron continued to provide air defence for Hollandia and Tadji throughout early May. From 7 to 10 May a detachment of 16 Kittyhawks from No. 78 Squadron operated from the Hollandia beachhead; owing to food shortages in the area the pilots arrived with rations for four days loaded in their aircraft. On 15 May the unit moved permanently to an airfield near Hollandia, from which it escorted USAAF bombers and formed part of the force protecting the US Army landings at Wakde on 17 May and Biak on the 27th. Overall, the squadron flew 601 sorties during May. Its operations over Biak included its only air-to-air combat of the war. On 3 June, 16 Kittyhawks from No. 78 Squadron intercepted a group of 12 Nakajima Ki-43 fighters and two Nakajima B5N bombers near Biak. The Australian airmen downed five Ki-43s and two B5Ns for the loss of one Kittyhawk and its pilot. This was the last major air battle fought by the RAAF during the Pacific War. On 10 June, eight No. 78 Squadron Kittyhawks were escorting a convoy when they sighted a Japanese Kawasaki Ki-61 fighter. Two of the Australian aircraft attacked the Ki-61 and shot it down near Japen Island. This was the final aerial victory achieved by the RAAF during the New Guinea campaign. No. 78 Squadron continued to fly defensive patrols over Hollandia until 20 July, when it was redeployed to Noemfoor island. This was the squadron's sixth move in nine months, and the intensive effort needed to pack and unpack stores on each occasion caused widespread fatigue among airmen and ground crew.