  We construct two complex-conjugated rigid surfaces with $p_g=q=2$ and $K^2=8$
whose universal cover is not biholomorphic to the bidisk. We show that these
are the unique surfaces with these invariants and Albanese map of degree $2$,
apart the family of product-quotient surfaces constructed by Penegini. This
completes the classification of surfaces with $p_g=q=2, K^2=8$ and Albanese map
of degree $2$.
