  A \emph{square} is a finite non-empty word consisting of two identical
adjacent blocks. A word is \emph{square-free} if it does not contain a square
as a factor. In any finite word one may delete the repeated block of a square,
obtaining thereby a shorter word. By repeating this process, a square-free word
is eventually reached, which we call a \emph{reduct} of the original word.
  How many different reducts a single word may have? It is not hard to prove
that any binary word has exactly one reduct. We prove that there exist ternary
words with arbitrarily many reducts. Moreover, the function counting the
maximum number of reducts a ternary word of length $n$ may have grows
exponentially. We also prove that over four letters, there exist words with any
given number of reducts, which does not seem to be the case for ternary words.
Finally, we demonstrate that the set of all finite ternary words splits into
finitely many classes of \emph{related} words (one may get from one word to the
other by a sequence of square reductions and factor duplications). A few open
questions are posed concerning some structures on words defined with the use of
the square reduction.
