Summary: It is well known that, without the assumption of independence between two nonnegative random variables \(X\) and \(Y\), the survival function of \(X\) is not identifiable on the basis of the joint distribution function of \(Z = \min(X, Y)\) and \(\delta = I(Z = Y)\). In this paper, we provide a simple condition in the form of conditional distribution of \(Y\) given \(X\). We show that our condition is equivalent to the constant-sum condition proposed by J. S. Williams and S. W. Lagakos [Biometrika 64, 215–224 (1977; Zbl 0366.92009)]. As a result the survival function of \(X\) can be identified from the joint distribution of \(Z\) and \(\delta\) and the Kaplan-Meier estimator with Greenwood’s formula for its variance remains valid. Examples which satisfy the condition are given.