  We present a construction of the superspace of maximally supersymmetric
adS_{p+2} x S^{d-p-2} near-horizon geometry based entirely on the supergravity
constraints of which the bosonic space is a solution. Besides the geometric
superfields, i.e. the vielbeine and the spinconnection, we also derive the
isometries of the superspace together with the compensating tangent space
transformations to all orders in anticommuting superspace coordinates.
