  In a 3-wave mixing process occurring in some nonlinear optical medium when
}$a_{1}^{\dagger}${\small mode interacts with both }$a_{2}^{\dagger}% ${\small
mode and }$a_{3}^{\dagger}${\small mode, we theoretically study the squeezing
effect generated by the operator }$S_{3}\equiv \exp[\mu(a_{1}%
a_{2}-a_{1}^{\dagger}a_{2}^{\dagger})+\nu(a_{1}a_{3}-a_{1}^{\dagger}%
a_{3}^{\dagger})]${\small . The new 3-mode squeezed vacuum state in Fock space
is derived, and the uncertainty relation for it is demonstrated, It turns out
that }$S_{3}${\small may exhibit enhanced squeezing. By virtue of the technique
of integration within an ordered product (IWOP) of operators, we also derive
}$S_{3}${\small 's normally ordered expansion. The Wigner function of new
3-mode squeezed vacuum state is calculated by using the Weyl ordering
invariance under similar transformations.
