This paper proposes a new method for measuring the dependency between securities. Applying independent component analysis to the return data of the whole component securities in a universe, independent factors composing the returns are extracted. Reconstructing return data of individual component security based on such factors, we find that each security has a unique factor hierarchy. A comparative analysis of the hierarchies can find dependence structures between securities. Empirical studies show that the new method outperforms old measures based on correlation, and that it reveals very delicate dependence structures which otherwise remain hidden. Useful examples of applying it to the portfolio or risk management are also provided.