Combine butter and sugar in a large mixing bowl, mixing well. Add eggs and vanilla; beat until well blended.
Sift together flour, baking powder, and salt in a small mixing bowl. Gradually add to creamed mixture, stirring well. Stir in pecans. Spread mixture in a greased 9-inch square pan. Bake at 350° for 30 minutes. Cool brownies completely in pan, and cut into 1 1/2-inch squares.