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We develop a new and more general formula for the construction of two dimensional nodal Riemann solver for a cell-centered Lagrangian scheme[1-2] developed by Make and his co-workers which allows us to use general one dimensional Riemann solvers that have intermediate velocity and pressure in the construction.The old formula for the scheme used in the papers of Maire et al is only a special case of our new formula.We present an entropy discussion, which indicates that the schemes with nodal solvers constructed following the old formula, which can only use the 1D Riemann solvers satisfying our strong entropy condition, are usually numerically very dissipative.