  A standard reconfigurable intelligent surface (RIS) can be configured to
reflect signals from an arbitrary impinging direction to an arbitrary outgoing
direction. However, if a signal impinges from any other direction, said signal
is reflected, with full beamforming gain, to a specific direction, which is
easily determined. The goal of this paper is to propose a RIS which \emph{only}
reflects signals from the configured impinging direction. This can be
accomplished by a RIS architecture that permutes the antenna elements in the
sense that a signal is re-radiated from a different antenna than the one
receiving the signal. We analytically prove this fact, and also discuss several
variants and hardware implementations.
