  The tau decays to four hadrons have been studied with the CLEO III detector
at the Cornell Electron Storage Ring (CESR) using (7.56 +- 0.15) fb^{-1} of
data collected near the Y(4S) resonance. We present the first statistically
significant measurements of B(tau- -> K- pi+pi- pi0 nu, excluding K^0) = (7.4
+- 0.8 +- 1.1) x 10^{-4} and B(tau--> K- K+ pi- pi0 nu) = (5.5 +- 1.4 +- 1.2) x
10^{-5}, including the first observation of the decay, tau- -> K- omega nu,
with branching fraction (4.1 +- 0.6 +- 0.7) x 10^{-4}. We also publish the
first upper limit for B(tau- -> K- K+ K- pi0 nu) < 4.8 (6.1) x 10^{-6} at 90%
(95%) confidence level (C.L.).
