With additional data and improved algorithms, we have enhanced the sensitivity of our appearance search for nu(mu) --> nu(tau) oscillations in the NOMAD detector in the CERN-SPS wide-band neutrino beam. The search uses kinematic criteria to identify nu(tau) charged current interactions followed by decay of the tau(-) to one of several decay modes. Our 'blind'' analyses of deep-inelastic scattering data taken in 1996 and 1997, combined with consistent reanalyses of previously reported 1995 data, yield no oscillation signal. For the two-family oscillation scenario, we present the contour outlining a 90% C.L. confidence region in the sin(2)2 theta(mu tau) - Delta m(2) plane. At large Delta m(2) the confidence region includes sin(2)2 theta(mu tau) < 1.2 X 10(-3) (a limit 3.5 times more stringent than in our previous publication), while at sin(2)2 theta(mu tau) = 1 the confidence region includes Delta m(2) < 1.2 eV(2)/c(4).