This paper explores the properties of the efficiency measures of the variant of radial measure (VRM) which is capable of dealing with negative data in DEA. We found that the input-oriented efficiency measure for VRM might be negative and the range of the output-oriented efficiency measure for VRM might be limited to [0.5, 1]. To circumvent these two situations, we propose the new efficiency measures which prevent the input-oriented efficiency from becoming negative and the output-oriented efficiency from being limited to [0.5, 1].