Sift together the flour, cocoa powder and baking powder.
Cream the butter and sugar together until fluffy.
Beat in the vanilla, then the eggs.
Fold in the flour mixture and walnuts and mix well.
Spoon the batter into a well-greased 20 cm./ 8 in.square baking tin and put into the oven preheated to moderate (180°C/350°F or Gas Mark 4).
Bake for 30 minutes or until firm.
Cut into squares to serve.