GRB 210421***A***, Swift-BAT refined analysis S. D. Barthelmy (GSFC), H. A. Krimm (NSF), S. Laha (GSFC/UMBC), A. Y. Lien (U Tampa), C. B. Markwardt (GSFC), D. M. Palmer (LANL), T. Parsotan (GSFC/UMBC), T. Sakamoto (AGU), M. Stamatikos (OSU) (i.e. the Swift-BAT team): Using the data set from T-239 to T+963 sec from the recent telemetry downlink, we report further analysis of BAT GRB 210421***A*** (trigger #1044426) (NAME, et al., GCN Circ. xxxx). The BAT ground-calculated position is RA, Dec = 104.883, 4.929 deg which is RA(J2000) = 06h 59m 32.0s Dec(J2000) = +04d 55' 42.8" with an uncertainty of 1.1 arcmin, (radius, sys+stat, 90% containment). The partial coding was 44%. [Description about the mask-weighted light curve] T90 (15-350 keV) is 79.2 +- 26.8 sec (estimated error including systematics). The time-averaged spectrum from T-21.7 to T+73.2 sec is best fit by a simple power-law model. The power law index of the time-averaged spectrum is 2.14 +- 0.13. The fluence in the 15-150 keV band is 2.2 +- 0.2 x 10^-06 erg/cm2. The 1-sec peak photon flux measured from T+2.47 sec in the 15-150 keV band is 2.0 +- 0.3 ph/cm2/sec. All the quoted errors are at the 90% confidence level. The results of the batgrbproduct analysis are available at http://gcn.gsfc.nasa.gov/notices_s/1044426/BA/