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If your Yorkie's coat is dry or has a skin condition that requires moisturizing, buy a spritzing coat conditioner to use before brushing. This helps strengthen the coat and avoid damage from splitting or tearing hairs. If your Yorkie's coat is naturally oily, you can skip conditioning since it might just weigh his coat down. You can also make your own conditioner. Mix 5 parts water and 1 part dog coat conditioner in a spritzer bottle. Use a pin brush without rubber back, which has metal tip without plastic covering, as they tear the coat. Divide an area of your dog's coat into sections and brush from the root to tip with the lie of the hair. Brushing against the lie of the coat is uncomfortable and can lead to tangles. Proper brushing will condition your dog's hair by spreading natural oils throughout your dog's coat.  A rubber backed brush can tear your Yorkie's coat. You might want to start brushing an area like the shoulder where your dog is less sensitive and ticklish. If you find small knots, work away at them with your fingers, teasing the knot apart. If it is stubborn and can't be worked out, use a comb and slide it between the base of the knot and the skin. Position a pair of scissors above the comb and snip the knot away. The comb protects the skin and keeps you from accidentally snipping it when the knot is raised.  Look for knots in areas where the fur rubs together such as the armpits, groin and behind the ears. Check under the tail to make sure there is no fecal soiling in the fur around the anus. If there is, consider bathing your dog, or snipping the soiled hair off if the soiling is extreme. Use a comb to gently comb out the fur of your dog's face and ears. Work slowly and pay attention to if your dog starts moving so you don't accidentally poke him in the eye with the comb. You can also clean any buildup from around the rims of your dog's eyes using eye wipes. Be careful so you don't get the wipe into the eye, which can sting.

Summary:
Condition your dog's coat. Brush sections of your dog's coat. Work out any knots. Comb around your dog's face and ears.