  We construct a duality functor in the category of continuous representations
of the Lie superalgebra E(4,4), the only exceptional simple linearly compact
Lie superalgebra, for which it wasn't known. This is achieved by constructing a
Lie conformal superalgebra of type (4,4), for which E(4,4) is the annihilation
algebra. Along the way we obtain an explicit realization of E(4,4) by vector
fields on a (4|4)-dimensional supermanifold.
