On that day, during a battle for a ridge near Ishimmi on Okinawa in the Ryukyu Islands, he exposed himself to enemy fire and charged the Japanese positions alone.
Sergeant Muller's official Medal of Honor citation reads: He displayed conspicuous gallantry and intrepidity above and beyond the call of duty.
When his platoon was stopped by deadly fire from a strongly defended ridge, he directed men to points where they could cover his attack.
Then through the vicious machinegun and automatic fire, crawling forward alone, he suddenly jumped up, hurled his grenades, charged the enemy, and drove them into the open where his squad shot them down.
Muller crawled forward through the flying bullets and explosives, then leaping to his feet, hurling grenades and firing his rifle, he charged the Japs and routed them.