Another potential source of tear staining is fleas. If you read the directions on most flea shampoos they suggest starting the shampoo with the head. Another problem that comes with fleas is ear mites. These are carried by the fleas. Ear mites can cause severe ear infections and as a result tear staining.
Fleas require a pro-active approach to keep under control.
Otherwise it will just come back and many times it will be worse than before. Once the source of excessive tearing and staining is found a pro-active program to remove the staining can begin. After insuring that health, irritation, environment, water and diet issues have been eliminated as a source of excessive tearing you can begin to think about removing the tear staining. Tetracycline I have found success in eliminating tear staining by putting my Maltese on a ten day course of low dose chlortetracycline or tetracycline. Occasionally this may need to be repeated.