  We show that the Lawrence--Krammer representation is unitary. We explicitly
present the non-singular matrix representing the sesquilinear pairing invariant
under the action. We show that reversing the orientation of a braid is
equivalent to the transposition of its Lawrence--Krammer matrix followed by a
certain conjugation. As corollaries it is shown that the characteristic
polynomial of the Lawrence--Krammer matrix is invariant under substitution of
its variables with their inverses up to multiplication by units, and is not a
complete conjugacy invariant for braids.
