Cream butter in a large mixing bowl. Add sugar, syrup, and egg yolks; beat well. Gradually add flour, stirring well.
Shape dough into 1-inch balls. Dip each ball into lightly beaten egg whites; roll in pecans, coating well.
Place 2 inches apart on lightly greased cookie sheets. Press a cherry half into center of each cookie. Bake at 325° for 20 to 25 minutes. Cool slightly on cookie sheets. Remove to wire racks to cool completely.