In a saucepan, cover the orange pieces with cold water and bring to a boil. Drain and repeat three times. (The blanching makes the oranges less bitter.) Set aside.
In the same saucepan, bring the water, sugar and corn syrup to a boil, stirring until the sugar dissolves. Add the blanched oranges. Bring to a boil, lower the heat and simmer gently until thick, about 1 1/2 hours. Strain into a container.
Place all the fruit and 180 ml (3/4 cup) of the cooking syrup in a blender. Purée until smooth. Strain. Let cool. Cover and refrigerate until well chilled.
Recipes with the "Healthy Pick" stamp have been evaluated by a registered dietitian member of the Ordre professionnel des diététistes du Québec.