The purpose of this article is to present another extension of some types of operators define on complex Hilbert space which is adjointable normal power operators depended on some characterization of normal operator with some modification of this operator which is essential it is up on adjoint of operator  and in this article we also, proven some important essential properties of this new class of adjointable operator, moreover, also we submitted the direct sum and tensor product of finite sets of  this classify of operators in this paper.