Bring 1 inch of water to a boil in a wide saucepan. In a large stainless steel bowl, whisk the egg whites with the sugar, water and corn syrup until blended. Set the bowl over the saucepan and whisk the whites until the sugar is completely melted, 4 to 5 minutes. Rub some of the mixture between your fingers to be sure it's not gritty.
Remove the bowl from the saucepan and add the cream of tartar to the whites. Using a standing electric mixer, beat the egg whites at medium speed for 1 minute to break them up. Gradually increase the speed to high and beat until the icing is fluffy, firm and no longer warm to the touch, about 10 minutes. Beat in the vanilla. Use right away.