  Let $k$ be a perfect field of characteristic $p$. Associated to any
(1-dimensional, commutative) formal group law of finite height $n$ over $k$
there is a complex oriented cohomology theory represented by a spectrum denoted
$E(n)$ and commonly referred to as Morava $E$-theory. These spectra are known
to admit $E_\infty$-structures, and the dependence of the $E_\infty$-structure
on the choice of formal group law has been well studied (cf.\ [GH], [R], [L],
Section 5, [PV]). In this note we show that the underlying homotopy type of
$E(n)$ is independent of the choice of formal group law.
