  The well known elliptic discrete Painlev\'e equation of Sakai is constructed
by a standard translation on the $E_8^{(1)}$ lattice, given by nearest neighbor
vectors. In this paper, we give a new elliptic discrete Painlev\'e equation
obtained by translations along next-nearest-neighbor vectors. This equation is
a generic (8-parameter) version of a 2-parameter elliptic difference equation
found by reduction from Adler's partial difference equation, the so-called Q4
equation. We also provide a projective reduction of the well known equation of
Sakai.
