The paper presents an improved HLL-Riemann solver that restores the contact surface, which was previously missing in the original HLL solver. This improved solver, called HLLC, is based on the same principles as the original HLL solver. The paper also presents new methods for estimating wave speeds. The resulting HLLC solver is as accurate and robust as the exact Riemann solver, but it is simpler and more computationally efficient, especially for non-ideal gases. The improved solver is implemented in the second-order WAF method and tested for one-dimensional problems with exact solutions and for a two-dimensional problem with experimental results. The HLL-Riemann solver was introduced by Harten et al. (1983) as an approximate method for solving the Riemann problem. It assumes a wave configuration consisting of two waves separating three constant states. This approach ignores the existence of intermediate waves and requires estimates for the speeds of the two assumed waves. While this approach is correct for two-equation systems like the shallow water equations, it is not correct for larger systems like the Euler equations. More recently, Davis (1988) and Einfeldt (1988) have used these ideas in the context of the Euler equations by proposing wave-speed estimates and carrying out computations. The resulting algorithms are efficient, robust, and simple. However, they have a major drawback: they destroy contact surfaces. This is due to the neglect of the intermediate wave in the local Riemann problem. For certain applications, such as combustion problems, this defect can have undesirable consequences. In this paper, an improved version of the HLL-Riemann solver is presented by restoring the contact surface. This is achieved by applying the same principles as Harten et al. (1983). The resulting HLLC-Riemann solver is implemented in the WAF method, a second-order TVD method of the Godunov type. Numerical results for one- and two-dimensional gas dynamics problems are presented for both ideal and covolume gases.The paper presents an improved HLL-Riemann solver that restores the contact surface, which was previously missing in the original HLL solver. This improved solver, called HLLC, is based on the same principles as the original HLL solver. The paper also presents new methods for estimating wave speeds. The resulting HLLC solver is as accurate and robust as the exact Riemann solver, but it is simpler and more computationally efficient, especially for non-ideal gases. The improved solver is implemented in the second-order WAF method and tested for one-dimensional problems with exact solutions and for a two-dimensional problem with experimental results. The HLL-Riemann solver was introduced by Harten et al. (1983) as an approximate method for solving the Riemann problem. It assumes a wave configuration consisting of two waves separating three constant states. This approach ignores the existence of intermediate waves and requires estimates for the speeds of the two assumed waves. While this approach is correct for two-equation systems like the shallow water equations, it is not correct for larger systems like the Euler equations. More recently, Davis (1988) and Einfeldt (1988) have used these ideas in the context of the Euler equations by proposing wave-speed estimates and carrying out computations. The resulting algorithms are efficient, robust, and simple. However, they have a major drawback: they destroy contact surfaces. This is due to the neglect of the intermediate wave in the local Riemann problem. For certain applications, such as combustion problems, this defect can have undesirable consequences. In this paper, an improved version of the HLL-Riemann solver is presented by restoring the contact surface. This is achieved by applying the same principles as Harten et al. (1983). The resulting HLLC-Riemann solver is implemented in the WAF method, a second-order TVD method of the Godunov type. Numerical results for one- and two-dimensional gas dynamics problems are presented for both ideal and covolume gases.