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In [5], together with J. C. Wood, the authors gave a completely explicitformula for all harmonic maps from $2$-spheres to the unitary group $U(n)$ interms of freely chosen meromorphic functions on $S^2$. The simplest harmonicmaps are the isotropic ones. Using Morse theory Burstall and Guest [1] showedthat the harmonic maps come in clusters labeled by the isotropic ones. In thiswork, using the formula for harmonic maps aforementioned, we describeexplicitly this procedure, showing how all harmonic maps can be built from theisotropic ones.  [1] F.~E.\ Burstall and M.~A.\ Guest, \textit{Harmonic two-spheres in compactsymmetric 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.

A note on the spectral deformation of harmonic maps from the two-sphere into the unitary group