  We interpret a class of 4k-dimensional instanton solutions found by Ward,
Corrigan, Goddard and Kent as four-dimensional instantons at angles. The
superposition of each pair of four-dimensional instantons is associated with
four angles which depend on some of the ADHM parameters. All these solutions
are associated with the group $Sp(k)$ and are examples of Hermitian-Einstein
connections on $\bE^{4k}$. We show that the eight-dimensional solutions
preserve 3/16 of the ten-dimensional N=1 supersymmetry. We argue that under the
correspondence between the BPS states of Yang-Mills theory and those of
M-theory that arises in the context of Matrix models, the instantons at angles
configuration corresponds to the longitudinal intersecting 5-branes on a string
at angles configuration of M-theory.
