We present the result of our most recent search for T violation in 205Tl, which is interpreted in terms of an electric dipole moment of the electron d(e). We find d(e) = (6.9 +/- 7.4)x10(-28)e cm, which yields an upper limit /d(e)/ < or = 1.6x10(-27)e cm with 90% confidence. The present apparatus is a major upgrade of the atomic beam magnetic-resonance device used to set the previous limit on d(e).