The handmade Persian carpet is famous worldwide not only for its elegant design and artistic structure, but also for its brilliant color harmony and incomparable raw materials. Various natural dyes accompanied by different mordants are used on various woolen yarns to obtain a wide range of unrepeatable shades for carpet. In this article, as a first step, the diversity of the undyed woolen yarns used in Persian carpets was statistically investigated by implementation of the Principle Component Analysis. Then the second derivative of Kubelka-Munk function of samples dyed with madder was considered to reach a pattern for identifying madder. The results show that, although the spectral reflectance of different selected woolen yarns has at least 3 dimensions, all derivative curves are qualitatively very similar with the same minimum and maximum peaks at 510 and 605 nm, respectively. The findings are confirmed when various types of madder were used in the dyeing process. As a result, it is shown that the nondestructive derivative spectrophotometry is able to identify madder on alum mordanted woolen yarns used in Persian carpets and to eliminate the effect of substrate. It is a useful technique for preservation, conservation, and dissemination of the Persian carpet.