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.