A bivariate extreme value distribution with fixed marginals is generated by a one-dimensional map called a dependence function. This paper proposes a new nonparametric estimator of this function. Its asymptotic properties are examined, and its small-sample behaviour is compared to that of other rank-based and likelihood-based procedures. The new estimator is shown to be uniformly, strongly convergent and asymptotically unbiased. Through simulations, it is also seen to perform reasonably well against the maximum likelihood estimator based on the correct model and to have smaller L1, L2 and L∞ errors than any existing nonparametric alternative. The n½ consistency of the proposed estimator leads to nonparametric estimation of Tawn's (1988) dependence measure that may be used to test independence in small samples.