An improved curve-fitting method for a simultaneous measurement of the real and imaginary parts of the complex refractive index of turbid media is demonstrated. Based on an introduction of angle-dependent light penetration into turbid media by Calhoun et al (2010 Opt. Lett. 35 1224), the fitting is performed on the rapid change part of the measured curve around the critical angle. Moreover, a technology to locate this part of the curve by differentiation is introduced. Experimental results on Intralipid solutions show that this method can significantly reduce the computation time as well as the fitting error between the measured curve and theoretical one.