  A new version of differential renormalization is presented. It is based on
pulling out certain differential operators and introducing a logarithmic
dependence into diagrams. It can be defined either in coordinate or momentum
space, the latter being more flexible for treating tadpoles and diagrams where
insertion of counterterms generates tadpoles. Within this version, gauge
invariance is automatically preserved to all orders in Abelian case. Since
differential renormalization is a strictly four-dimensional renormalization
scheme it looks preferable for application in each situation when dimensional
renormalization meets difficulties, especially, in theories with chiral and
super symmetries. The calculation of the ABJ triangle anomaly is given as an
example to demonstrate simplicity of calculations within the presented version
of differential renormalization.
