This does not sound like eczema but is probably a condition called seborrhoeic dermatitis. Wash your baby's scalp regularly with a baby shampoo such as Elizabeth Anne. Apply a very mild cortisone cream such as Mylocort once daily to the worst parts of the rash until it clears up. This rash should clear up by itself after the age of 6 months. Do not use the Mylocort for more than 5 days at a time.If your baby's rash does not clear up with this treatment please ask your paediatrician to see him.
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