Well, crap! You can't use cornstarch because you are allergic to corn. What do you do?
You can try the recipe without the cornstarch. Or you can substitute cornstarch in the recipe with few other starches instead.
Here are a few examples to get you started.
Arrowroot Starch is a little sweeter tasting but works well for thickening soups and such. The only downside is that the foods don't save overnight in the fridge the same. I really like it in breads or biscuits that I've tried making with it. It seems to help hold the breads together better.
Potato Starch seems to be the best option for most things. Soups last overnight better. My taste-tester said that she doesn't notice a difference in the bread taste or texture when I used potato starch (I am allergic to potato).
Tapioca Starch wasn't my favorite for soups but it wasn't bad either. I liked it for making my homemade baking powder pretty well. It does great in sweeter tasting things, like pudding. I only used it in bread once and the bread came out fine.
Sweet White Rice Flour is one of my favorites for substituting in gravies for. It thickens up quickly and smoothly with almost no problems about clumping up. The gravies come out smooth and with a nice flavor.
Tip for substituting cornstarch
Don't be afraid to play with the different starches you find. You may find that you love one for your veggie soup but like another one for your chicken soup. One might be your favorite for biscuits. Or you might find that you like the flavor of both starches in a soup.
Don't be afraid to get crazy in the kitchen and mix them up! Try them out and let us know what you used them in and how you liked them.