Preheat oven to 350 degrees F (175 degrees C), and grease an 8x8 inch square baking dish (or larger).
Stir together the gluten-free baking mix, cornstarch, white sugar, brown sugar, cocoa powder, and baking soda in a bowl, sifting with a fork to remove lumps. Pour in the eggs and melted margarine, and mix with a large spoon or electric mixer on low until the mixture forms a smooth batter, 3 to 5 minutes. Scrape the batter into the prepared baking dish.
Place a sheet of aluminum foil on the oven rack to prevent spills as the brownies rise, then fall during baking. Bake until a toothpick inserted in the center of the brownies comes out clean, 40 to 45 minutes.