The singularity of meromorphic functions of finite positive order in the unit circle

By using Ahlfors' covering surface theory,the existence theorem of maximum type Borel point of meromorphic functions of finite positive order in the unit circle dealing with small functions which extend the result of G.Valiron,and make the result of M.Tsuji into the corollary of the result of this paper and the equivalent theorem of the existence are obtained.