  We propose a new unified evolution equation for parton distribution functions
appropriate for both large and small Bjorken variables $x$, which is an
improved version of the Ciafaloni-Catani-Fiorani-Marchesini equation. In this
new equation the cancellation of soft divergences between virtual and real
gluon emissions is explicit without introducing infrared cutoffs,
next-to-leading contributions to the Sudakov resummation can be included
systematically. It is shown that the new equation reduces to the
Dokshitzer-Gribov-Lipatov-Altarelli-Parisi equation at large $x$, to the
Balitsky-Fadin-Kuraev-Lipatov (BFKL) equation at small $x$, and to the modified
BFKL equations with a dependence on momentum transfer $Q$ and with unitarity,
if hard virtual gluon contributions and correction to strong rapidity ordering
are retained, respectively.
