In summary, this communication reports so-called `centrosymmetric' crystals of a Zn(II) complex, which is indicated surprisingly to have crystallized with a residual non-centrosymmetry in space group C2/c based on the observation of SHG. A small excess of polarity packing in the otherwise centrosymmetric single crystals appears to result in a large second-order nonlinearity which can be further enhanced by increasing the strain caused by the UV light exposure. These led to a strong dependence of χ(2) on the inhomogeneity created by the induced strain. The induced strain varies with temperature, as indicated from the temperature-dependent SHG measurements. By increasing the temperature from 10 to 50 K, a sharp increase in the SHG signal is followed by a slow decrease to its minimum at ∼ 175 K. A further increase in the temperature to 300 K is accompanied by a slow increase in the SHG signal. The underlying mechanism has been discussed.