  A Monte Carlo generator has been constructed to simulate the reaction e^+e^-
\to \gamma + 4 \pi, where the photon is assumed to be observed in the detector.
Only initial state radiation is considered. Additional collinear photon
radiation has been incorporated with the technique of structure functions.
Predictions are presented for cms energies of 1GeV, 3GeV and 10GeV,
corresponding to the energies of DAPHNE, BEBC and of B-meson factories. The
event rates are sufficiently high to allow for a precise measurement of R(Q^2)
in the region of Q between approximately 1GeV and 2.5GeV. For the construction
of the program we employ isospin relations between the amplitudes governing tau
decays into four pions and electron positron annihilation into four pions.
Estimates of the kinematic breaking of these isospin relations as a consequence
of the \pi^- -- \pi^0 mass difference are given.
