  Using the data from SuperKamiokande, Kamiokande and Homestake solar neutrino
experiments we derive an upper bound on the magnetic moment of the neutrino and
find $\mu_{\nu_e}\leq(2.2-2.3)\times 10^{-10}\mu_{B}$, within four different
standard solar models. We assume equal magnetic moments for all neutrino
flavours. This limit is obtained when neutrinos do not undergo any
"disappearence" mechanism other than the magnetic moment conversion due to the
solar magnetic field and for a total or nearly total suppression of the
intermediate energy neutrinos. In our work we consider an energy dependent
suppression of solar neutrinos. We also point out that the limit may be further
reduced if the detector threshold energy in $\nu_{e,x}e^{-}$ scattering with
solar neutrinos is decreased.
