In Wenneker et al. [Computation of compressible flows on unstructured staggered grids. In: Onate E, Bugeda G, Suarez B, editors. Proceedings European Congress on Computational Methods in Applied Sciences and Engineering, ECCOMAS 2000, Barcelona, 11-14 September 2000, Barcelona, 2000. CIMNE. http://ta.twi.tudelft.nl/users/wesseling/pub.html] an unstructured staggered scheme for the two-dimensional (2D) Euler equations is discussed. Such a scheme cannot be in classic conservation form for momentum. The aim of the present paper is to formulate a generalized conservation form for momentum on unstructured staggered grids, and to demonstrate by numerical experiments that the scheme satisfies the Rankine-Hugoniot conditions. Numerical results for 1D Riemann problems on 2D unstructured grids confirm that the scheme converges to the entropy solution. In addition, transonic flow around an airfoil is computed.