Building a relativistic magnetohydrodynamic (RMHD) codes based on upwind schemes is a challenging project, because the characteristic wave structures for RMHDs has not yet been analytically given. We obtained an analytic expression of eigenvalues and eigenvectors of the flux Jacobian matrix of RMHDs for one-dimensional, isothermal flows with two velocity and magnetic field components (that is, x and y components only), which can be used to build numerical codes. The degeneracies were taken into account. Here, we present preliminary test results with an RMHD code based on the total variation diminishing (TVD) scheme.