Combine all of the ingredients in a blender set on high speed for 15-30 seconds.
The original recipe here and in the books includes real egg white, but, after many suggestions from readers I have replaced that with 1/4 cup egg substitute, which is mostly egg white and does a great job of making the drink foamy. If you like, you can instead use 2 tablespoons of the drink foam product Frothee. This is available in many supermarket liquor sections or in liquor stores. Or, if it's all you've got available, you can still use 1 egg white from a large egg as originally specified in the recipe.
Notice the egg whites in the recipe. That's how you get a frothy, foamy drink. If you want a version of Strawberry and Pineapple Julius, check out the recipes in More Top Secret Recipes.