  We consider a position-dependent quantum walk on ${\bf Z}$. In particular, we
derive a detection method for edge defects by embedded eigenvalues of its time
evolution operator. In the present paper, the set of edge defects is that of
points in ${\bf Z}$ on which the coin operator is an anti-diagonal matrix. In
fact, under some suitable assumptions, the existence of a finite number of edge
defects is equivalent to the existence of embedded eigenvalues of the time
evolution operator.
