There have been many suggestions about babies suffering from eczema to try a home remedy called diluted bleach bath. Simply it is putting a little bleach such as Clorox in lukewarm water at bath time and allowing your baby to soak in it for about five minutes. If your baby is experiencing some skin irritation from the bleach, please discontinue. Definitely consult with your pediatrician about this. Because eczema in babies is such a delicate condition, this may not be helpful in all cases. Some other skin irritations may have some benefits to a diluted bleach bath.
Personally, I have notice that going to the pool could be helpful alternative to a bleach bath. I saw areas on my daughter that were severe, improving after going swimming about twice week. I do recommend to moisturize your baby skin at least three times a day depending on the severity of the eczema. Eczema in babies requires constant moisture and very prone to flare up from the smallest allergic reaction.