  Using the DIANA data on the charge-exchange reaction $K^+n \rightarrow pK^0$
on a bound neutron, in which the s-channel formation of the pentaquark baryon
$\Theta^+(1538)$ has been observed, we analyze the dependence of the
background-subtracted $\Theta^+ \rightarrow pK^0$ signal on the $K^0$ emission
angle in the $pK^0$ rest frame. In order to describe the observed
$\cos\Theta_K^\mathrm{cms}$ distribution, invoking the interference between the
nonresonant s-wave and the $\Theta^+$-mediated higher-wave contributions to the
amplitude of the charge-exchange reaction is required at a 2.8$\sigma$ level.
The spin--parity assignment of 1/2$^-$ for the $\Theta^+$ baryon is ruled out
at a statistical level of 2.9 standard deviations. A physically-meaningful
selection in $\cos\Theta_K^\mathrm{cms}$ based on the observed angular
dependence of the $\Theta^+ \rightarrow pK^0$ signal allows to boost the
statistical significance of the signal up to 7.1 standard deviations. This is
far in excess of previously reported signals and renders the $\Theta^+$
existence more credible.
