Abstract: In this paper a new randomized response device including Warner’s (1965) and Horvitz, Shah and Simmons’ (1967) devices as special case is proposed. This method is more efficient than Warner’s and Mangat’s (1990) randomized devices. When considering incomplete truthful answers come from respondents, under the condition that the probability of truthful report answer in present method is larger than one in preceding methods, the method in this paper is superior to Simmons’ and Sarjinder Singh’s (2000) methods without sacrificing respondent protection and at no additional sampling cost. Under simple random sampling scheme without replacement and unknown proportion of population possessing neutral attribute, the optimal allocation of sizes of two sub-samples is given.