  We prove some epsilon regularity results for n-dimensional minimal two-valued
Lipschitz graphs. The main theorems imply uniqueness of tangent cones and
regularity of the singular set in a neighbourhood of any point at which at
least one tangent cone is equal to a pair of transversely intersecting
multiplicity one n-dimensional planes, and in a neighbourhood of any point at
which at which at least one tangent cone is equal to a union of four distinct
multiplicity one n-dimensional half-planes that meet along an (n-1) -
dimensional axis. The key ingredient is a new Excess Improvement Lemma obtained
via a blow-up method (inspired by the work of L. Simon on the singularities of
`multiplicity one' classes of minimal submanifolds) and which can be iterated
unconditionally. We also show that any tangent cone to an n-dimensional minimal
two-valued Lipschitz graph that is translation invariant along an (n-1) or
(n-2)- dimensional subspace is indeed a cone of one of the two aforementioned
forms, which yields a global decomposition result for the singular set
