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We use the contact invariant defined in [2] to construct a new invariant ofLegendrian knots in Kronheimer and Mrowka's monopole knot homology theory(KHM), following a prescription of Stipsicz and V\'ertesi. Our Legendrianinvariant improves upon an earlier Legendrian invariant in KHM defined by thesecond author in several important respects. Most notably, ours is preserved bynegative stabilization. This fact enables us to define a transverse knotinvariant in KHM via Legendrian approximation. It also makes our invariant amore likely candidate for the monopole Floer analogue of the "LOSS" invariantin knot Floer homology. Like its predecessor, our Legendrian invariant behavesfunctorially with respect to Lagrangian concordance. We show how this fact canbe used to compute our invariant in several examples. As a byproduct of ourinvestigations, we provide the first infinite family of nonreversibleLagrangian concordances between prime knots.

Invariants of Legendrian and transverse knots in monopole knot homology