Numerical simulation of the propagation of electrical signals in the heart is a very demanding application. In fact, very fine meshes and small time steps are currently required to capture the phenomena. In this paper, we propose and explore a very high-order scheme specifically designed for this application. Its numerical properties are detailed and the different choices on both the scheme’s definition and implementation are discussed and justified. Numerical results show the importance of considering very high-order schemes, even for classical tests such as the propagation of planar or spiral waves.