  We study the off-diagonal blocks in the M(atrix) model that are supposed to
correspond to open strings stretched between a Dp-brane and a Dp'-brane. It is
shown that the spectrum, including the quantum numbers, of the zero modes in
the off-diagonal blocks can be determined from the index theorem and unbroken
supersymmetry, and indeed reproduces string theory predictions for p-p'
strings. Previously the matrix description of a longitudinal fivebrane needed
to introduce extra degrees of freedom corresponding to 0-4 strings by hand. We
show that they are naturally associated with the off-diagonal zero modes, and
the supersymmetry transformation laws and low energy effective action
postulated for them are now derivable from the M(atrix) theory.
