We compare an entropy estimator recently discussed by Zhang ( 2012 ) with two estimators, and , introduced by Grassberger ( 2003 ) and Schürmann ( 2004 ). We prove the identity , which has not been taken into account by Zhang ( 2012 ). Then we prove that the systematic error (bias) of is less than or equal to the bias of the ordinary likelihood (or plug-in) estimator of entropy. Finally, by numerical simulation, we verify that for the most interesting regime of small sample estimation and large event spaces, the estimator has a significantly smaller statistical error than .