To improve extremely dry skin on a 4-month-old baby, you can try giving the baby a bath every 3 days instead of every 2 days. Use a warm, damp washcloth without soap or any other product to gently cleanse the face and skin every night. During bath time, do not use any product on the skin. Instead, you can apply a little grapeseed or olive oil on the skin before drying it with a towel. This will help to create a barrier against dryness. Give it a try and see how it helps with hydrating the skin.
