We present a search for charged Higgs bosons in decays of pair-produced top quarks using $109.2\ifmmode\pm\else\textpm\fi{}5.8{\mathrm{pb}}^{\ensuremath{-}1}$ of data recorded from $p\overline{p}$ collisions at $\sqrt{s}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1.8\mathrm{TeV}$ by the D0 detector during 1992--1996 at the Fermilab Tevatron. No evidence is found for charged Higgs production, and most parts of the $[{M}_{{H}^{+}},\mathrm{tan}\ensuremath{\beta}]$ parameter space where the decay $t\ensuremath{\rightarrow}{H}^{+}b$ has a branching fraction close to or larger than that for $t\ensuremath{\rightarrow}{W}^{+}b$ are excluded at $95%$ confidence level. Assuming ${m}_{t}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}175\mathrm{GeV}$ and $\ensuremath{\sigma}(p\overline{p}\ensuremath{\rightarrow}t\overline{t})\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}5.5\mathrm{pb}$, for ${M}_{{H}^{+}}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}60\mathrm{GeV}$, we exclude $\mathrm{tan}\ensuremath{\beta}<0.97$ and $\mathrm{tan}\ensuremath{\beta}>40.9$.