  Recently in \cite{Anderson:2013zia, Anderson:2013ila}, it was shown that
global de Sitter space is unstable even to the massive particle creation with
no self-interactions. In this paper we study the instability by making use of
the coordinate-independent plane wave in de Sitter space, within this
formalism, we show that the previous results of instability of de Sitter space
due to the particle creation can be generalized to higher-spin fields in a
straightforward way. The so-called plane wave are defined globally in de Sitter
space and de Sitter invariance is manifest since such modes are deduced from
the group theoretical point of view by the means of the Casimir operators. In
fact, we employ the underling symmetry of embedding space namely the $4+1$
dimensional flat space to write the field equations and the solutions can be
obtained in terms of the plane wave in embedding space.
