  The existence of the well-known Jacquet-Langlands correspondence was
established by Jacquet and Langlands via the trace formula method in 1970. An
explicit construction of such a correspondence was obtained by Shimizu via
theta series in 1972. In this paper, we extend the automorphic descent method
of Ginzburg-Rallis-Soudry to a new setting. As a consequence, we recover the
classical Jacquet-Langlands correspondence for PGL(2) via a new explicit
construction.
