  The problem of holomorphic contractibilty of the Teichmuller spaces $T(0, n)$
of punctured spheres ($n > 4$) arose in the 1970s in connection with solving
algebraic equations in Banach algebras. Recently it was solved by the author in
\cite{Kr2}.
  In the present paper we improve the statement of Lemma 3 in \cite{Kr2} and
provide an alternate proof of holomorphic contractibility of low dimensional
Teichmuller spaces.
