This paper describes the development and evaluation of a new beamforming strategy based on pixel-based focusing for ultrasound linear array systems. We first implement conventional pixel-based beamforming in which the transmitted wave is assumed as spherical and diverging from the centre of the transmit subaperture. This assumed wave-shape is only valid within a limited angle on each side of the beam and this restricts the number of different subaperture positions from which data can be combined to improve image quality. By analyzing the field patterns, we propose a new unified pixel-based beamforming algorithm that better adapts to the non-spherical wave-shape of the transmit beam. This approach enables us to select the best-possible signal from each transducer waveform for data superposition. In simulations and a phantom study, we show that the unified pixel-based beamformer offers significant improvements in image quality compared to other delay-and-sum methods but at a higher computational cost. The new algorithm also demonstrates robust performance in a limited in vivo study. Overall, the results show that it is potentially of value in clinical applications.