New measure of unbiased multifractality in signals of finite length for the generalized Hurst exponent language is introduced. The measure is based on the observation of the whole generalized Hurst exponent h(q) range instead of looking just at the edge behavior h^±=h(q→± ∞). Such approach seems to be particularly useful in cases when h(q) is not a monotonic function of the deformation parameter (moment order) q, for instance in non-stationary signals. The method is then applied in finances to search for the existence and properties of multifractal asymmetry between positive and negative returns for various world stock indices. Results are then compared to the usual multifractal analysis within MF-DFA.

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