In-phase waves and echo waves are commonly existing in coupled systems. In Physica D 151 (2001) 199 we proved existence of echo waves in linearly coupled oregonators and showed that the echo waves may coexist with the stable homogeneous positive steady state. This Letter develops a different approach (so-called "reducing dimension") compared with our "mode decomposition" method of stability of in-phase waves in Phys. Lett. A 301 (2002) 231, and rigorously proves stability of the echo waves. The method can be easily applied to other similar systems.