The Savoie Flag (above) is a white cross with a red background, the cross is reaching the sides of the flag.
Do not get confused with the square Swiss flag with a small white cross in the red.
In 1315, Amédée V from Savoie, Count of Savoie from 1285 to 1323, helped the St Jean Chevaliers in Rhodes and together they won again the Muslims. It is even possible that after the death of the Great master of St Jean Chevaliers, Amédée took his weapons and decided to become the leader of his army. And also used their flag (the flag of St Jean de Jérusalem, Rhodes and Malta are similars).