Can you over Ozonate your water???

Is it possible to ozonate your water too much? I had a water ozonator that I used for years, then one day it went bad and I could not smell the ozone anymore. Recently, I took it apart. They are relatively simple and I figured out that the "ozonating tube" (I can't remember the technical name of the part) was bad. I found another one on ebay and ordered it. I put it in and it worked fine. I cant remember the output designation but the new "tubes" rating was at least 10 times the output of the old, and it is significantly larger in size also. So...is it possible that I could ozonate my water too much and it actually be harmful to me?