  We construct an exactly solvable spin-orbital model on a decorated square
lattice that realizes an SU(2)-invariant Majorana spin liquid with parton Fermi
surfaces, of the kind discussed recently by Biswas et al. [ Phys. Rev. B. {\bf
83}, 245131(2011)]. We find power-law spin correlations as well as power-law
spin-nematic correlations with the same dominant $1/|{\bf r}|^3$ envelope. The
model is solvable also in the presence of Zeeman magnetic field. One fermion
species carries $S^z=0$ quantum number and its Fermi surface is not altered in
the field, while the Fermi surfaces of the other species evolve and can
disappear. In particular, we find an interesting half-magnetization plateau
phase in which spin excitations are gapful while there remain spinless gapless
excitations that still produce metal-like thermal properties. In the
fully-magnetized phase, the model reduces to the one proposed by Baskaran et
al., [arXiv:0908.1614v3] in terms of the orbital degrees of freedom.
