  We examine the theta-expansion of the eleven-dimensional supervielbein. We
outline a systematic procedure which can be iterated to any order. We give
explicit expressions for the vielbein and three-form potential components up to
order ${\cal O}(\th^5)$. Furthermore we show that at each order in the number
of supergravity fields, in a perturbative expansion around flat space, it is
possible to obtain exact expressions to all orders in theta. We give the
explicit expression at linear order in the number of fields and we show how the
procedure can be iterated to any desired order. As a byproduct we obtain the
complete linear coupling of the supermembrane to the background supergravity
fields, covariantly in component form. We discuss the implications of our
results for M(atrix) theory.
