A class of chaotic map called piecewise-quadratic-equation map to design feedback stream cipher is proposed. Such map can generate chaotic signals that have uniform distribution function, δ-like autocorrelation function. Compared with the piecewise-linear map, this map provides enhanced security in that they can maintain the original perfect statistical properties, as well as overcome the defect of piecewise-linearity and expand the key space. This paper presents a scheme to improve the local complexity of the chaotic stream cipher based on the piecewise-quadratic-equationmap. Both the theoretic analysis and the results of simulation show that this scheme improves the microstructure of the phase-space graph on condition that the good properties of the original scheme are remained. This map can generate chaotic signals that have uniform distribution function, δ-like autocorrelation function. Compared to the piecewise-linear map, this map provides enhanced security in that they can maintain the original perfect statistical properties, as well as overcome the defect of piecewise-linearity and expand the key space. This paper presents a scheme to improve the local complexity of the chaotic stream cipher based on the piecewise-quadratic- equationmap. Both the theoretic analysis and the results of simulation show that this scheme improves the microstructure of the phase-space graph on condition that the good properties of the original scheme are remained.