The electric form factor of the neutron was determined from measurements of the d-->(e-->,e'n)p reaction for quasielastic kinematics. Polarized electrons were scattered off a polarized deuterated ammonia (15ND3) target in which the deuteron polarization was perpendicular to the momentum transfer. The scattered electrons were detected in a magnetic spectrometer in coincidence with neutrons in a large solid angle detector. We find G(n)(E)=0.0526+/-0.0033(stat)+/-0.0026(sys) and 0.0454+/-0.0054+/-0.0037 at Q(2)=0.5 and 1.0 (GeV/c)(2), respectively.