We have measured transport properties of a two-dimensional array of small Josephson junctions with normal-state tunneling resistance R(N)=60 k Omega. The zero-bias resistance showed a so-called square-root-cusp-type temperature dependence in a limited temperature range and the current-voltage characteristics were nonlinear at lower temperatures. We interpret these features as a precursor of the charge Kosterlitz-Thouless-Berezinskii transition with a finite screening length.