Preheat the oven to 375 degrees F (190 degrees C). Grease cookie sheets.
In a medium bowl, cream together the butter and sugar until smooth. Beat in the eggs, one at a time. Stir in the cornstarch, cream of tartar and baking powder until well blended. Roll the dough into 1 inch balls and place them 1 inch apart onto the prepared cookie sheets.
Bake for 10 to 12 minutes in the preheated oven, or until light brown. Remove to wire racks to cool.