  Suzuki's split-step quantum walk on the one-dimensional integer lattice can
be naturally viewed as a chirally symmetric quantum walk. Given the unitary
time-evolution of such a chirally symmetric quantum walk, we can separately
introduce well-defined indices for the eigenvalues $\pm 1.$ The bulk-edge
correspondence for Suzuki's split-step quantum walk is twofold. Firstly, we
show that the multiplicities of the eigenvalues $\pm 1$ coincide with the
absolute values of the associated indices. Note that this can be viewed as the
symmetry protection of bound states, and that the indices we consider are
robust in the sense that these depend only on the asymptotic behaviour of the
parameters of the given model. Secondly, we show that that such bound states
exhibit exponential decay at spatial infinity.
