This paper is an appendix to the paper \cite{Msadinv} written too late. Using
the technique developed in \cite{Msadinv} it gives an explicit formula for
certain invariant of $3$-ornaments of order $6$, which was guessed in \cite{V}
but whose existence remained only conjectural. Now the classification of
invariants of $3$-ornaments of order $6$, described in \cite{Mfinv} modulo this
conjecture, becomes complete.

\bibItem[M95]{Mfinv} A.B.Merkov, {\em Finite-order invariants of ornaments},
J. of Math. Sciences, vol.90, no.4 (1998), pp.2215--2273.

\bibItem[M00]{Msadinv} A.B.Merkov, {\em Segment-arrow Diagrams and Invariants
Of Ornaments}, Sbornik: Mathematics 191:11 pp.1635--1666.

\bibItem[V93]{V}  V.A.Vassiliev, {\em Invariants of ornaments}, in: {\em
Singularities and Bifurcations}, AMS, Advances in Soviet Math., vol.~21 (ed.
V.I.Arnold), Providence, RI, 1994, p. 225--261.