G.G. Hamedani - Department of Mathematics, Statistics, and Computer Science Marquette University, P.O. Box ۱۸۸۱, Milwaukee, WI ۵۳۲۰۱-۱۸۸۱, U.A.A.
Hans Volkmer - Department of Mathematical Sciences, University of Wisconsin-Milwaukee, Milwaukee, WI ۵۳۲۰۱, U.S.A.

It is well-known that i.i.d. (independent and identically distributed) normal random variables are transformed into i.i.d. normal random variables by any orthogonal transformation. Less well-known are nonlinear transformations with the above mentioned property, see [2]. In this work we present nonlinear transformations preserving normality, which are more general than the existing ones in the literature.