  The Yang-Baxter equation for a $SU(2)\times U(1)$-symmetric $S=1/2$
spin-orbital chain was solved using the special computer algorithm developed by
the author. The 8 new $R$-matrices separated on 5 groups are presented. Among
the obtained integrable models there are special cases related to 1D
ferromagnet ${\rm TDAE-C}_{60}$, 1D superconductors ${\rm AC}_{60}$ (A=K, Cs,
Rb), the quarter filled ladder compound ${\rm NaV}_2{\rm O}_5$ and the model of
correlated electrons on a chain of Berry phase molecules.
