  Given a quiver, Nakajima introduced the quiver variety and the Hecke
correspondence, which is a closed subvariety of Cartesian products of quiver
varieties. In this paper, we consider two nested quiver varieties as fiber
products of Hecke correspondences along natural projections. After blowing up
the diagonal, we prove that they are isomorphic to a quadruple moduli space
which Negu\c{t} observed for the Jordan quiver. The main ingredient is Jiang's
derived projectivization theory and Hekking's derived blow-up theory, while we
obtain the local model when both the two derived schemes are quasi-smooth.
