  We write supersymmetry preserving conditions for infinite M5-branes
intersecting on a (3+1)-dimensional space. In contrast to previously known
solutions, these intersections are completely localized. We solve the equations
for a particular class of configurations which in the near-horizon decoupling
limit are dual to N_f = 2N_c Seiberg-Witten superconformal field theories with
gauge group SU(N) and generalisations to SU(N)^n. We also discuss the
relationship to D3-branes in the presence of an A_k singularity.
