We discuss the approximation of the solution of the multidimensional Riemann problem by a Roe type method. In a first part, we show that the exact solution of the problem obeys, for small times, a jump relation that generalizes exactly the one that helps to define the Roe averaged matrix in 1D. We show that the new linearization of Roe, Deconinck and Struijs does not follow this jump relation. Then, we show that there exists, in general, a solution to the problem. In a second part, we show the existence and unicity of the solution of the linearized hyperbolic Riemann problem, and, recalling the results of \citeabgrall, we give its analytic solution. Then we provide some indications on how all this can be used in a numerical scheme.