For the two-sample model with proportional hazard, i.e., for \(\bar G(x)=1-G(x)=[\bar F(x)]^{\theta}=[1-F(x)]^{\theta}\), \(x\in R\), \(\theta >0\), the problem of estimating the relative risk \((\theta)\) is considered for the conventional uncensored data model. This model corresponds to the classical Cox regression model [\textit{D. R. Cox}, J. R. Stat. Soc., Ser. B 34, 187-220 (1972; Zbl 0243.62041)] when the concomitant variate can assume only two values, 0 and 1. A two-step estimator of \(\theta\) is considered. \({\tilde \theta}\), an initial estimator of \(\theta\) is based on the identity \(\bar FdG=\bar GdF\), and this is incorporated in the formulation of the final step estimator. This two-step estimator and the Cox partial maximum likelihood estimator of \(\theta\) share the minimum asymptotic variance property within the class of all rank based regular estimators of the relative risk.