  Hu, Paz and Zhang [ B.L. Hu, J.P. Paz and Y. Zhang, Phys. Rev. D {\bf 45}
(1992) 2843] have derived an exact master equation for quantum Brownian motion
in a general environment via path integral techniques. Their master equation
provides a very useful tool to study the decoherence of a quantum system due to
the interaction with its environment. In this paper, we give an alternative and
elementary derivation of the Hu-Paz-Zhang master equation, which involves
tracing the evolution equation for the Wigner function. We also discuss the
master equation in some special cases.
