In this paper we have proposed an improved miniaturization design of a rectangular microstrip patch antenna based on Minkowski fractal. The design methodology consists in considering a rectangular patch on which the conventional and modified Minkowski curve are successively applied until the second iteration. In total, three miniaturized antennae are proposed. They are structured by a fractal patch engraved on an FR-4 epoxy substrate. Design and simulation are performed by CADFEKO 7.0.1 software, better suited for small size antennae. The proposed miniaturized fractal models operate at the same frequency F= 15.53 GHz, as the conventional Rectangular Microstrip patch antenna. Moreover, each of them enables a good impedance matching, as can be confirmed by the low return loss obtained (< -15 dB) at the same resonance frequency. The proposed antennae presented a significant size reduction of 89.76 % for Minkowski model, 88.8 % and 86% for both modified Minkowskimodels when compared to the conventional inset-fed rectangular patch antenna. Overall, our study illustrated that, after a modified Minkowski miniaturization technique was introduced a better performance and impedance matching was achieved. According to the IEEE Standard Classification of Satellite Frequency Bands, the results of the miniaturized and optimized fractal patch antenna can effectively contribute to Ku-band communications.