  We introduce a class of F-theory vacua which may be viewed as a
specialization of the so-called $E_6$ fibration, and construct a weak coupling
limit associated with such vacua which we view as the `square' of the Sen
limit. We find that while Sen's limit is naturally viewed as an orientifold
theory, the universal tadpole relation which equates the D3 charge between the
associated F-theory compactification and the limit we construct suggests that
perhaps the limiting theory is in fact an oriented theory compactified on the
base of the F-theory elliptic fibration.
