  We show that, with the exception of the words $a^2ba^2$ and $b^2ab^2$, all
(finite or infinite) binary patterns in the Prouhet-Thue-Morse sequence can
actually be found in that sequence as segments (up to exchange of letters in
the infinite case). This result was previously attributed to unpublished work
by D. Guaiana and may also be derived from publications of A. Shur only
available in Russian. We also identify the (finitely many) finite binary
patterns that appear non trivially, in the sense that they are obtained by
applying an endomorphism that does not map the set of all segments of the
sequence into itself.
