In a sample survey, questions requiring personal or controversial assertions often give rise to resistance. A randomised response procedure can be used to help the researcher gather accurate data in this case. This paper describes a new two-stage unrelated randomised response procedure that combines the use of two randomisation devices (Mangat & Singh, 1990) and an unrelated question (Horwitz et al. 1967). It examines the situation where the respondents are not completely truthful in their answers. The efficiency of this new method is compared with the original one-stage procedure proposed by Horwitz et al. (1967), and guidelines for choosing the values of different parameters for the procedures are provided. Results from an empirical study which examines the efficiency and feasibility of the proposed method are given.