The optically pumped cesium (Cs) frequency standard at the National Research Laboratory of Metrology, Ibaraki, Japan (NRLM), NRLM-4, was modified in various ways in order to improve frequency stability and accuracy, We determined the frequency stability by comparing the phase with that of a hydrogen maser: the Allan deviation was /spl sigma//sub y/(/spl tau/)=5/spl times/10/sup -13///spl radic//spl tau/. We estimated the frequency corrections and uncertainties due to various sources, and the total uncertainty was found to be 2.9/spl times/10/sup -14/. The frequency difference between NRLM-4 and the international atomic time (TAI) was also measured.