  We present an extension of the non-crossing approximation (NCA), which is
widely used to calculate properties of Anderson impurity models in the limit of
infinite Coulomb repulsion $U\to\infty$, to the case of finite $U$. A
self-consistent conserving pseudo-particle representation is derived by
symmetrizing the usual NCA diagrams with respect to empty and doubly occupied
local states. This requires an infinite summation of skeleton diagrams in the
generating functional thus defining the ``Symmetrized finite-U NCA'' (SUNCA).
We show that within SUNCA the low energy scale $T_K$ (Kondo temperature) is
correctly obtained, in contrast to other simpler approximations discussed in
the literature.
