Estimating the number of signals (NIS) is an important goal in array signal processing, such as direction-of-arrival (DOA) estimation. A common approach for solving this problem is to use an eigenvalue of the array covariance matrix and information criterion, such as the Akaike information criterion (AIC) and minimum description length (MDL). However they suffer serious degradation, when the incoming signals are coherent. To estimate the NIS of the coherent signals impinging on a uniform linear array (ULA), a method for estimating the number of signals without eigendecomposition (MENSE) is proposed. The accuracy of the NIS estimation performance of MENSE is superior to the other algorithms equipped with preprocessing such as the spatial smoothing preprocessing (SSP) and forward/backward spatial smoothing techniques (FBSS) to decorrelate the coherency of signals. Instead of using SSP or FBSS preprocessing, MENSE uses the Hankel correlation matrices. The Hankel correlation matrices can not only decorrelate the coherency of signals but also suppress the influence of noise. However, in severe conditions like low signal-to-noise ratio (SNR) or a closely spaced signals impinging on a ULA, the NIS estimation metric of MENSE has some bias which causes estimation error. In this paper, we pay attention to the multiplicity defined by the ratio of the geometric mean to the arithmetic mean. Accordingly, we propose a new estimation metric that has less bias than that in MENSE. The Computer simulation results show that the proposed method is superior to MENSE in the above severe conditions.