  We provide an alternative proof for the capacity region of the degraded
Gaussian multiple-input multiple-output (MIMO) broadcast channel. Our proof
does not use the channel enhancement technique as opposed to the original proof
of Weingertan {\it et. al.} and the alternative proof of Liu {\it et. al}. Our
proof starts with the single-letter description of the capacity region of the
degraded broadcast channel, and directly evaluates it for the degraded Gaussian
MIMO broadcast channel by using two main technical tools. The first one is the
generalized de Bruijn identity due to Palomar \emph{et. al.} which provides a
connection between the differential entropy and the Fisher information matrix.
The second tool we use is an inequality due to Dembo which lower bounds the
differential entropy in terms of the Fisher information matrix.
