  Connected components of $\Map(S^4,B\SU(2))$ are the classifying spaces of
gauge groups of principal $\SU(2)$-bundles over $S^4$. Tsukuda [Tsu01] has
investigated the homotopy types of connected components of $\Map(S^4,B\SU(2))$.
But unfortunately, the proof of Lemma 2.4 in [Tsu01] is not correct for $p=2$.
In this paper, we give a complete proof. Moreover, we investigate the further
divisibility of $\epsilon_i$ defined in [Tsu01]. In [Tsu], it is shown that
divisibility of $\epsilon_i$ have some information about $A_i$-equivalence
types of the gauge groups.
