  We extend the well-known 't Hooft anomaly matching conditions for continuous
global symmetries to discrete groups. We state the matching conditions for all
possible anomalies which involve discrete symmetries explicitly. There are two
types of discrete anomalies. For Type I anomalies, the matching conditions have
to be always satisfied regardless of the details of the massive bound state
spectrum. The Type II anomalies have to be also matched except if there are
fractionally charged massive bound states in the theory. We check discrete
anomaly matching in recent solutions of certain N=1 supersymmetric gauge
theories, most of which satisfy these constraints. The excluded examples
include the chirally symmetric phase of N=1 pure supersymmetric Yang-Mills
theories described by the Veneziano-Yankielowicz Lagrangian and certain
non-supersymmetric confining theories. The conjectured self-dual theories based
on exceptional gauge groups do not satisfy discrete anomaly matching nor
mapping of operators, and are viable only if the discrete symmetry in the
electric theory appears as an accidental symmetry in the magnetic theory and
vice versa.
