A 6 MV tandem accelerator at the University of Tsukuba, Japan, has been working on multi-nuclide (Be-10, C-14, Al-26, Cl-36, Ca-41, and I-129) accelerator mass spectrometry (AMS) since 2016. This paper reports improvement of isobar suppression techniques for Cl-36 AMS. Previous studies have shown that a Cu sample holder with AgBr backing is the most suitable for Cl-36 AMS to decrease isobaric S-36 interference. Therefore, the method of AgBr preparation was considered, and we found that preparation under acidic conditions was most appropriate to reduce S-36 in Cl-36 AMS. CI charge states and their analysis method were considered to improve peak separation. Cl-36(8+) was chosen for detection because it allows clear separation of S-36 from the Cl-36 spectrum. Furthermore, S-36 spectrum tails could be removed using a third anode (dE3) signal. As a result, a Cl-36/Cl background of 3 x 10(-15) was achieved.