A two-dimensional mapping system derived from the coupled-chaos system is studied by means of numerical calculations and analytical methods. The mapping system shows the chaos-chaos transition through intermittency. Near the transition point the numerically obtained power spectrum has an inverse power-law dependence for small frequencies. Moreover, the distribution function of the state variable which exhibits the intermittent behavior shows an inverse power-law. These numerical results are analyzed by introducing a multiplicative noise model. Satisfactory agreements of the results obtained from the multiplicative noise model with those of numerical calculations are obtained.