Preheat the oven to 325 degrees F (165 degrees C). Grease an 8x8 inch baking dish.
In a medium bowl, stir together the sugar, cocoa powder and yogurt. Stir in the eggs one at a time until well blended, then add vanilla and salt. Stir in the flour until just absorbed. Spread evenly into the prepared pan.
Bake for 28 to 32 minutes in the preheated oven, until the brownies begin to pull away from the sides of the pan, and a toothpick inserted comes out fairly clean (sticky crumbs are okay). Cool brownies in the pan over a wire rack before cutting into squares. Cover tightly with plastic wrap to store.
