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 $cosTheta_K^mathrm{cms}$ 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 $cosTheta_K^mathrm{cms}$ 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.
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