Can't cancel eng. light????

Eng. light is on, code given...secondary O2 sensor problem, the one behind the cat. conv... changed it out and cancelled code eng. light off. three starts and eng. light came back on with same code for same O2 sensor. change out O2 sensor again cancelled light then 3 starts light came back on same code for same O2 sensor. Each time code was checked O2 sensor output was confirmed as good???? anyone with any ideas.

what exact code are you getting? The problem could be an issue with the wiring/circuit to the sensor, or a problem with the catalytic converter tripping an O2 code. Post the actual DTC you're getting so we can help you better without guessing.

check the wiring to the O2 sensor