In a saucepan, mix the sugar and cornstarch; gradually stir in the water. Cook over medium heat, stirring constantly, until mixture thickens and boils.
Boil for one minute. Slowly stir half of the hot mixture into slightly beaten egg yolks. Blend that into hot mixture in saucepan. Boil one minute longer; stirring constantly.
Remove from heat; continue stirring until smooth. Blend in butter and lemon juice.
Pour into baked 9-inch pie shell.
For meringue: Beat egg whites, cream of tartar, and water until frothy. Gradually beat in sugar; continue beating until stiff and glossy. (Do not underbeat). Pile meringue on top of hot lemon mixture; seal meringue onto the edge of the crust to prevent shrinking and weeping.
Bake in a 400° oven until the color is a delicate brown (8 to 10 minutes).