  The shuffle product \(u\shuffle v\) of two words \(u\) and \(v\) is the set
of all words which can be obtained by interleaving \(u\) and \(v\). Motivated
by the paper \emph{The Shuffle Product: New Research Directions} by Restivo
(2015) we investigate a special case of the shuffle product. In this work we
consider the shuffle of a word with itself called the \emph{self shuffle} or
\emph{shuffle square}, showing first that the self shuffle language and the
shuffle of the language are in general different sets. We prove that the
language of all words arising as a self shuffle of some word is context
sensitive but not context free. Furthermore, we show that the self shuffle \(w
\shuffle w\) uniquely determines \(w\).
