The diet of a healthy non-human animal is supplemented with a melatonin-containing supplement by providing a dietary supplement containing melatonin in an amount from about 0.1 mg to about 12 mg/kg of body weight of the animal and administering the dietary supplement to the animal at a regular interval. The selected interval may be daily, weekly, monthly, or seasonally. The melatonin-containing supplement is in the form of a pill, a tablet, a capsule, a powder, a liquid, or is incorporated into food or food pellets. The method is practiced on cats and dogs.