Abstract <p>In this paper, the Kendall correlation coefficient is studied in the continuous case. In the beginning of the paper, we consider the Pearson correlation coefficient ρ and its sample analog ρ_<i>n</i>, which is a good approximation for ρ for large <i>n</i> since it converges to ρ in probability. We further discuss the Kendall rank correlation coefficient τ_<i>n</i> and its theoretical analog τ. In the continuous case, τ_<i>n</i> is defined in the terms of ranks of the concomitants of order statistics. It is shown that <i>E</i>τ_<i>n</i> = τ and that τ_<i>n</i> converges in probability to τ. Thus, the coefficient τ_<i>n</i> is also a good approximation for τ, as is the case with the coefficients ρ_<i>n</i> and ρ. This detection explains the reason that τ can also be considered as a theoretical correlation coefficient. In many works, τ is used as a theoretical correlation coefficient without explanations as to why it can be considered as such. Since the coefficient τ has been little studied, we then discuss the basic properties of τ, its advantages and disadvantages and compare it with coefficient ρ. Among the advantages of τ we stress that τ exists for any continuous distributions. Some examples are given at the end of the paper.</p>