  Using data from the CLEO II detector at CESR, we measure ${\cal
B}(\tau^\pm\rightarrow h^\pm\pi^0\nu_\tau)$ where $h^\pm$ refers to either
$\pi^\pm$ or $K^\pm$. We use three different methods to measure this branching
fraction. The combined result is ${\cal B}(\tau^\pm\rightarrow
h^\pm\pi^0\nu_\tau) = 0.2587 \pm 0.0012 \pm 0.0042$, in good agreement with
Standard Model predictions. This result, in combination with other precision
measurements, reduces the significance of the one-prong problem in tau decays.
A postscript version is available through World-Wide-Web in
http://w4.lns.cornell.edu/public/CLNS/1994/
