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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 bythe author. The 8 new $R$-matrices separated on 5 groups are presented. Amongthe obtained integrable models there are special cases related to 1Dferromagnet ${\rm TDAE-C}_{60}$, 1D superconductors ${\rm AC}_{60}$ (A=K, Cs,Rb), the quarter filled ladder compound ${\rm NaV}_2{\rm O}_5$ and the model ofcorrelated electrons on a chain of Berry phase molecules.Comment: 10 page

R-matrices for integrableSU(2) ×U(1)-symmetric spin-orbital chains