Preheat the oven to 190 degrees C. Grease baking trays.
In a medium bowl, cream together the butter and sugar until smooth. Beat in the eggs, one at a time. Stir in the cornflour, cream of tartar and baking powder until well blended. Roll the dough into 2cm-sized balls (approx) and place them 3cm apart onto the prepared baking trays.
Bake for 10 to 12 minutes in the preheated oven, or until light brown. Cool on wire racks.