  The structure of the coincidence symmetry group of an arbitrary
$n$-dimensional lattice in the $n$-dimensional Euclidean space is considered by
describing a set of generators. Particular attention is given to the
coincidence isometry subgroup (the subgroup formed by those coincidence
symmetries which are elements of the orthogonal group). Conditions under which
the coincidence isometry group can be generated by reflections defined by
vectors of the lattice will be discussed, and an algorithm to decompose an
arbitrary element of the coincidence isometry group in terms of reflections
defined by vectors of the lattice will be given.
