In this paper, we discuss the deficiencies of normal form definitions based on Functional Dependency and introduce a new normal form concept based on Functional Independency. Functional Independency has not been systematically investigated while there is a very strong theoretical foundation for the study of Functional Dependency in relational database normalization. This paper will demonstrate that considering Functional Dependency alone cannot eliminate some common data anomalies and the normalization process can yield better database designs with the addition of Functional Independency.