Using the upgraded Beijing Spectrometer, we have measured the total cross section for e(+)e(-) annihilation into hadronic final states at center-of-mass energies of 2.6, 3.2, 3.4, 3.55, 4.6, and 5.0 GeV. Values of R, sigma(e(+)e(-)-->hadrons)/sigma(e(+)e(-)-->&mgr;(+)&mgr;(-)), are determined.