  We consider a series of Mott insulators in unit of two orbitals each hosting
spin-1/2 electron, and by pairing two spin-1/2 into spin-1 triplet, derive the
effective exchange interaction between the adjacent units via fourth order
perturbation theory. It turns out that the biquadratic exchange interaction
between spin-1, which is one of the origins of the nematic order, arises only
in processes where the four different electrons exchange cyclically along the
twisted loop, which we call "twisted ring exchange" processes. We show that the
term becomes the same order with the Heisenberg exchange interactions when the
on-orbital Coulomb interaction is not too large. Whereas, the inter-orbital
Coulomb interactions give rise to additional processes that cancel the twisted
ring exchange, and strongly suppresses the biquadratic term. The Mott insulator
with two electrons on degenerate two orbitals is thus not an ideal platform to
study such nematic orders.
