  We solve the several complex variables preSchwarzian operator equation
$[Df(z)]^{-1}D^2f(z)=A(z)$, $z\in \C^n$, where $A(z)$ is a bilinear operator
and $f$ is a $\C^n$ valued locally biholomorphic function on a domain in
$\C^n$. Then one can define a several variables $f\to f_\alpha$ transform via
the operator equation
$[Df_\alpha(z)]^{-1}D^2f_\alpha(z)=\alpha[Df(z)]^{-1}D^2f(z)$, and thereby,
study properties of $f_\alpha$. This is a natural generalization of the one
variable operator $f_\alpha(z)$ in \cite{DSS66} and the study of its univalence
properties, e.g., the work of Royster \cite{Ro65} and many others. M\"{o}bius
invariance and the multivariables Schwarzian derivative operator of T. Oda
\cite{O} play a central role in this work.
