Preheat oven to 350°F (175°C). Grease an 8-inch square baking pan.
In a medium saucepan, melt the butter over low heat.
Stir in the cocoa powder until smooth.
Remove from heat and let cool slightly.
In a large bowl, combine the flour and baking powder. Beat in the eggs one at a time, then stir in the sugar and cooled chocolate mixture until blended.
Pour batter into prepared pan. Bake for 25 minutes or until a toothpick inserted into center comes out clean.