  Orthogonal sets of idempotents are used to design sets of unitary matrices,
known as constellations, such that the modulus of the determinant of the
difference of any two distinct elements is greater than $0$. It is shown that
unitary matrices in general are derived from orthogonal sets of idempotents
reducing the design problem to a construction problem of unitary matrices from
such sets. The quality of the constellations constructed in this way and the
actual differences between the unitary matrices can be determined algebraically
from the idempotents used.
  This has applications to the design of unitary space time constellations.
