In this paper we propose a new statistical concept called directed generalized measure of association (dGMA) to quantify the amount of association transferred between subsystems in a system evolving in time. This paper is an improvement of the previously established method called generalized measure of association (GMA) by taking the conditional dependence between time-delay representation of subsystems into account. Directed-GMA is a rank-based pair-wise measure which can deal with dynamic data sets. This is done by calculating the rank permutation in a conditional scheme under the framework of conditional causality. In this paper we present a bivariate case and assume that the cause-effect relationship is one directional, e.g. there is no feedback. The preliminary results on the synthetic data sets reveal that the proposed method is able to extract nonlinear causal relationship, which cannot be extracted by traditional approaches. To further assess the performance we compared the results with another rank-based method called symbolic transfer entropy (STE). Our approach can be a promising tool to infer causal relationship in complex systems, e. g. human brain, to reveal their underlying effective connectivity.