The purpose of this paper is to carry out a modification of the finite volume WENO (weighted essentially non-oscillatory) scheme of Titarev and Toro [10]. This modification is done by using the third order TVD flux [10] as building blocks in spatially fifth order WENO schemes, instead of the second order TVD flux proposed by Titarev and Toro. The resulting scheme improves both the original and Toros flux in terms of order of accuracy, convergence and better resolution of discontinuities. The numerical solution is advanced in time by TVD Runge-Kutta method. Extension to systems is carried out by the component-wise application of the scalar framework. Numerical experiments confirm the high resolution of the proposed scheme. Thus, a considerable amount of simplicity and robustness is gained while retaining the expected third-order resolution.