We study the following database design problem. Given a universal relation scheme 〈U, F〉 where F is a set of functional dependencies, find an in some way normalized database schema D = {〈X1, F1〉,..., 〈Xn, Fn〉} where Xi ⊂ U and Fi is inherited from F, such that D is an independent representation of the universal scheme 〈U, F〉. This means that D has both the lossless join property and the faithful closure property, (***** Fi)+ = F+, where + denotes the closure of a set of functional dependencies. We show that this goal can easily be achieved by an extension of the well-known synthetic approach of Bernstein and others to database design. We merely have to check whether the usual synthesis procedure has produced a key component 〈Xi, Fi〉 such that Xi → U ε F+; in case this is true the output of the synthesis procedure is actually an independent (and not only faithful) representation, otherwise we only have to add one further component, namely just a key. These claims are proved by a careful inspection of the Aho/Beeri/Ullman algorithm to test for losslessness. Finally, we show how to use our method to synthesize minimal independent third normal form schemas.