The main idea of this paper is to study the dependence between the probability of default and the recovery rate on credit portfolio and to seek empirically this relationship. We examine the dependence between PD and RR by theoretical approach. For the empirically methodology, we use the bootstrapped quantile regression and the simultaneous quantile regression. These methods allow to determinate the dependence between the PD and RR. This study is elaborated for a sample composed by 17 banks in Greece. The period of study is of 7 years (2006-2012). The measurement of this dependence is determinate by using 7 indicators: the probability of default, the recovery rate, the number of defaults, the expected value of losses, the growth rate of GDP in Greece and three dummy variables who the exit of another firm of the Athens Exchange, the new firm is quoted in the Athens exchange and the failure of Greece is declared. We use in our study two dependent variables PD and RR. The descriptive, correlation and regression analysis results are presented by STATA 12.