Unilateral successful number a(K

1

n) has been redefined in this paper: Suppose person a and b contest on complete graph K

p

.a first colors one of the edges of K

p

green

b then colors another edge red.a and b color the rest edge alternately.a wins the game if what a has colored forms a star K

1

n while b fails to.The smallest natural number P=P(n) for a to win the game is called the unilateral successful number

denoted a(K

1

n).The authors have proved that a(K

1

4) equals 7 by using exhaustive method.