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The analyzing power $A$ in 28-GeV/c proton-proton elastic scattering was measured with a polarized proton target and a high-intensity unpolarized proton beam at the Brook-haven National Laboratory alternating-gradient synchrotron. The ${{P}_{\ensuremath{\perp}}}^{2}$ range of 2.85 to 5.95 ${(\mathrm{G}\mathrm{e}\mathrm{V}/\mathit{c})}^{2}$ was covered with good precision. A small dip of about -3.5% was found near ${{P}_{\ensuremath{\perp}}}^{2}=3.5$ ${(\mathrm{G}\mathrm{e}\mathrm{V}/\mathit{c})}^{2}$ where a 24-GeV/c CERN experiment had reported a deep dip of about -16% with large errors. In the previously unexplored large-${{P}_{\ensuremath{\perp}}}^{2}$ region near 6 ${(\mathrm{G}\mathrm{e}\mathrm{V}/\mathit{c})}^{2}$ these new large-error points suggest that $A$ may be rising.