  In [5], together with J. C. Wood, the authors gave a completely explicit
formula for all harmonic maps from $2$-spheres to the unitary group $U(n)$ in
terms of freely chosen meromorphic functions on $S^2$. The simplest harmonic
maps are the isotropic ones. Using Morse theory Burstall and Guest [1] showed
that the harmonic maps come in clusters labeled by the isotropic ones. In this
work, using the formula for harmonic maps aforementioned, we describe
explicitly this procedure, showing how all harmonic maps can be built from the
isotropic ones.
  [1] F.~E.\ Burstall and M.~A.\ Guest, \textit{Harmonic two-spheres in compact
symmetric spaces, revisited}, Math. Ann. 309 (1997) 541--572.
  [5] M.~J. Ferreira, B.~A Sim\~oes and J.~C. Wood \emph{All harmonic
$2$-spheres in the unitary group, completely explicitly}, Math. Z. {\bf 266}
(2010), 953--978.
