In this work, we propose a method for calculating the real and imaginary part of the index of refraction N = n-ik and the film thickness d of absorbing thin films from normal incidence reflectance R and transmittance T measurements. The method determines the film thickness and the index of refraction values at all experimental points simultaneously, utilizing the fact that both the real and imaginary parts of the index of refraction are continuous functions. We test the ability of our method to extract correct d, n, and k values from two test datasets of R and T data generated from known n and k values. One of the test datasets contains random noise up to ±1.5% for R and ±0.5% for T, emulating random experimental errors. After verifying that our method is capable of accurate and reliable estimation of the index of refraction, we apply it to the determination of optical constants of thin films of the organic dye N,N′-dimethylperylene-3,4:9,10-dicarboximide.