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  1. The ratio of the electric to magnetic form factors of the proton, μpGEp/GMp, has been measured for elastic electron-proton scattering with polarized beam and target up to four-momentum transfer squared Q2=5.66(GeV/c)2 using double spin asymmetry for target spin orientation aligned nearly perpendicular to the beam momentum direction. This measurement of μpGEp/GMp agrees with the Q2 dependence of previous recoil polarization data and reconfirms the discrepancy at high Q2 between the Rosenbluth and the polarization-transfer method with a different measurement technique and systematic uncertainties uncorrelated to those of the recoil-polarization measurements. The form factor ratio at Q2=2.06(GeV/c)2 has been measured as μpGEp/GMp=0.720±0.176stat±0.039sys, which is in agreement with an earlier measurement using the polarized target technique at similar kinematics. The form factor ratio at Q2=5.66(GeV/c)2 has been determined as μpGEp/GMp=0.244±0.353stat±0.013sys, which represents the highest Q2 measurement reached using double spin asymmetries with polarized target to date.