  We show that the requirement of Poincare invariance (more specifically
invariance under boosts/rotations that mix brane directions with transverse
directions) places severe constraints on the form of actions describing
multiple D-branes, determining an infinite series of correction terms to the
currently known actions. For the case of D0-branes, we argue that up to field
redefinitions, there is a unique Lorentz transformation rule for the coordinate
matrices consistent with the Poincare algebra. We characterize all independent
Poincare invariant structures by describing the leading term of each and
providing an implicit construction of a Poincare invariant completion. Our
construction employs new matrix-valued Lorentz covariant objects built from the
coordinate matrices, which transform simply under the (extremely complicated)
Lorentz transformation rule for the matrix coordinates.
