  It is well known that Gaussian symplectic ensemble (GSE) is defined on the
space of $n\times n$ quaternion self-dual Hermitian matrices with Gaussian
random elements. There is a huge body of literature regarding this kind of
matrices. As a natural idea we want to get more universal results by removing
the Gaussian condition. For the first step, in this paper we prove that the
empirical spectral distribution of the common quaternion self-dual Hermitian
matrices tends to semicircular law. The main tool to establish the universal
result is given as a lemma in this paper as well.
