A method of beam design for a high-intensity focused ultrasound (HIFU) array transducer, a technology that has recently made significant progress, can be an essential tool to utilize the potential of an HIFU. A method of beam design that constrains the apodization weights of each element based on the least squares method was proposed to meet clinical needs in HIFU therapy in terms of the total power at the focal spot and the suppression of the near-field power density. The difficulty in calculation was solved with orthonormalized maps introduced using a fixed-point theorem. The proposed method was applied to the beamforming design to form a uniform wide beam and a Bessel beam with uniform phase shift as the optimized beam shapes. There was an improvement of approximately 20% in homogeneity and 70% in power efficiency. The proposed method has proven useful in forming a uniform wide beam, and the success of our method suggests its potential usefulness.