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Let $\Lambda$ be a Legendrian submanifold of the 1-jet space of a smoothmanifold. Associated to $\Lambda$ there is a Legendrian invariant calledLegendrian contact homology, which is defined by counting rigidpseudo-holomorphic disks of $\Lambda$. Moreover, there exists a bijectivecorrespondence between rigid pseudo-holomorphic disks and rigid Morse flowtrees of $\Lambda$, which allows us to compute the Legendrian contact homologyof $\Lambda$ via Morse theory.  If $\Lambda$ is spin, then the moduli space of the rigid disks can be given acoherent orientation, so that the Legendrian contact homology of $\Lambda$ canbe defined with coefficients in $\mathbb Z$. In this paper we give an explicitalgorithm for computing the corresponding orientation of the moduli space ofrigid Morse flow trees, using the Morse theoretical framework.

To compute orientations of Morse flow trees in Legendrian contact homology