<p>Recently (Ahmed et al. in Stat Theory Methods 47:324–343, 2018) have discussed the problem of estimating the means of two sensitive variables simultaneously by using two uncorrelated scrambling variables. In this study, we introduce a new idea that use of correlated scrambling variables in randomized response techniques play an important role to increase the efficiency of the estimators of population means of sensitive variables. We found that the simultaneous estimation of the means of the two sensitive variables by using two correlated scrambling variables results in gain in the efficiency of the estimators. This idea is appealing because it costs nothing to the investigator and does not effect the privacy of a respondent as well. Empirical evidences are given based on application to a real secondary data set.</p>