With the use of a quantity normally scaled in multifractals, a generalized form is postulated for entropy, namelySq ≡k [1 – ∑i=1W piq]/(q-1), whereq∈ℝ characterizes the generalization andpi are the probabilities associated withW (microscopic) configurations (W∈ℕ). The main properties associated with this entropy are established, particularly those corresponding to the microcanonical and canonical ensembles. The Boltzmann-Gibbs statistics is recovered as theq→1 limit.