Abstract:  Proved here is the theorem‚that‚if f is the holomorphic self-map in H（R _I ；R _I ） without fixed point in the first classical domain R _I and if f（B _nm ）⊂ B _nm ‚each convergent sub-array of map cluster｛f _n ｝iterates at a point on the conjunct boundary of R I and B _nm ‚where f _n is the nth iteration of f.

Key words:  holomorphic self-map, iteration, classical domain, Wolff point