  We analyze the guided modes in coupled waveguides made of negative-index
materials without gain or loss. We show that it supports non-Hermitian
phenomenon on the existence of guided mode versus geometric parameters of the
structure. The non-Hermitian effect is different from parity-time (PT)
symmetry, and can be explained by a simple coupled-mode theory with an anti-PT
symmetry. The existence of exceptional points and slow-light effect are
discussed. This work highlights the potential of loss-free negative-index
materials in the study of non-Hermitian optics.
