  Using the analytic extension method, we study Hawking radiation of an $(n +
4)$-dimensional Schwarzschild-de Sitter black hole. Under the condition that
the total energy is conserved, taking the reaction of the radiation of
particles to the spacetime into consideration and considering the relation
between the black hole event horizon and cosmological horizon, we obtain the
radiation spectrum of de Sitter spacetime. This radiation spectrum is no longer
a strictly pure thermal spectrum. It is related to the change of the
Bekenstein-Hawking(B-H) entropy corresponding the black hole event horizon and
cosmological horizon. The result satisfies the unitary principle. At the same
time, we also testify that the entropy of de Sitter spacetime is the sum of the
entropy of black hole event horizon and the one of cosmological horizon.
