  Quantum study of supersymmetric theories on Euclidean two dimensional anti-de
Sitter space (AdS$_2$) is invalid if we use the standard normalizable
functional basis due to its incompatibility with supersymmetry. We cure this
problem by demonstrating that supersymmetry requires complexified spectrum and
constructing the supersymmetric basis for scalar and spinor fields. Our new
basis is free of fermionic zero modes, delta-function normalizable with respect
to a newly defined inner product, and compatible with the supersymmetric
asymptotic boundary condition. We also explore the one-loop evaluation using
this basis and show that it agrees with the standard nonsupersymmetric basis up
to a global contribution arising from the fermion zero mode.
