  We present four infinite series of new quantum theories with super-Poincare
symmetry in six dimensions, which are not local quantum field theories. They
have string like excitations but the string coupling is of order one.
Compactifying these theories on $T^5$ we find a Matrix theory description of M
theory on $T^5$ and on $T^5/\IZ_2$, which is well defined and is manifestly
U-duality invariant.
