Well, I used this with my first maltese puppy and I saw very little improvement after 6 weeks. But then my puppy died

so I don't know if it would've completely cleared up or not. Now I have most of the bottle just sitting and collecting dust in my house because the maltese that I got after that puppy has no tear stains at all(thank God!). LOL
Angel Eyes works for some dogs, then again it doesn't work for others. There are many other natural ways to help with tear stains without putting antibiotics in there system. Read through this thread on the maltese forum about tear staining:
Spoiled Maltese - the largest maltese dog forum and website.
Here's another method:
Spoiled Maltese - the largest maltese dog forum and website
An quote from the site:
"Once your pup stops teething and you find he still has tearstain problems, you can try Tylan powder from your vet. Angel Eyes is a dilluted form of Tylan powder that contains both Tylan and beef liver to make it taste better. I would recommend going with the regular Tylan over the Angel Eyes because it is MUCH cheaper and seems to work faster. Usually you will do a 10-day course of the Tylan, and if the new growth doesn't come out white, you can do another 10-day course. After doing two courses, if there is still new staining, there is an underlying problem such as allergies, tear duct blockage, shape of the eye, eyelashes growing inward toward the eye, etc. Keep in mind that Tylan is an antibiotic and there may be long-term consequences that you will have to consider. Any of the topical eye treatments don't seem to work well, and this includes Eye Envy, Stay White, Angel Eyes, etc. I think only a few people have had long-term success with these methods.
Yes, a teaspoon of plain nonfat/lowfat (organic if available) yogurt can help improve the staining."
This is from a top maltese breeder website, basically explains more in detail causes and cures:
Tear Staining: The Causes & Cures
Hope this all helps!