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<正> Ⅰ. INTRODUCTION Let f（ζ） be the analytic and schhcht function in the unit disc U={ζ:|ζ|<1}, ζ1,ζ2 be any points in U, and f（ζ1） · f（ζ2） ≠ 1. We denote by B1 the family of all of such functions and call it Bieberbach family of functions.