  A Lorentz and gauge symmetry preserving regularization method is discussed in
four dimension based on momentum cutoff. We use the conditions of gauge
invariance or equivalently the freedom of shift of the loop momentum to define
the evaluation of the terms carrying even number of Lorentz indices, e.g.
proportional to $k_{\mu}k_{\nu}$. The remaining scalar integrals are calculated
with a four dimensional momentum cutoff. The finite terms (independent of the
cutoff) are free of ambiguities coming from subtractions in non-trivial cases.
Finite parts of the result are equal with the results of dimensional
regularization. The proposed method can be applied to various physical
processes where the use of dimensional regularization is subtle or a physical
cutoff is present. As a famous example it is shown that the triangle anomaly
can be calculated unambiguously with this new improved cutoff.
