Entropy measures of DNA sequences estimate their randomness or, inversely, their repeatability. L-block Shannon discrete entropy accounts for the empirical distribution of all length-L words and has convergence problems for finite sequences. A new entropy measure that extends Shannon�s formalism is proposed. Rényi�s quadratic entropy calculated with Parzen window density estimation method applied to Chaos Game Representation/Universal Sequence Map of DNA sequences constitute a novel technique to evaluate sequence global randomness without some of the former method drawbacks. The asymptotic behavior of this new measure was analytically deduced and the calculation of entropies for several synthetic and experimental biological sequences was performed. This new technique can be very useful in the study of DNA sequence complexity and provide additional tools for DNA entropy estimation.