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A concept of a lossless feeding network that allows for achieving unconstrained taper excitation in circularly polarized four-beam antenna arrays having arbitrary even number of radiating elements has been proposed. The proposed feeding network consists of a 4×4 Butler matrix and four identical N-way unequal-split power dividers connected at its outputs. It has been shown that by choosing the power division ratio of additional power dividers an arbitrary taper excitation can be achieved across the antenna array. The obtained taper is identical for all four beams by taking advantage of two-port circularly polarized antenna elements. The theoretical analysis followed by experimental results of reduced-sidelobe four-beam antenna array having six radiating elements has been presented.