A measurement of the tau(-)-> K-pi(0)nu(tau) branching fraction has been made using 230.2 fb(-1) of data recorded by the BABAR detector at the PEP-II e(+)e(-) collider, located at the Stanford Linear Accelerator Center (SLAC), at a center-of-mass energy root s close to 10.58 GeV. We measure B(tau(-)-> K-pi(0)nu(tau))=(0.416 +/- 0.003(stat)+/- 0.018(syst))%.