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A new easy-to-apply design procedure is proposed in this letter for constructing small wideband circularly polarized (CP) bidirectional and unidirectional square slot antennas. With an asymmetric T-shaped strip protruded from the signal line of the feeding coplanar waveguide (CPW) into the square slot, a reference antenna with a fractional 3-dB axial-ratio bandwidth (abbreviated as CPBW) of about 11% can be obtained. The proposed bidirectional CP slot antenna (BICPSA) can be modified from the reference antenna by stretching the left end of the T-shaped strip upward, by embedding a rectangular metal patch in the square slot, and by implanting a grounded metal strip from the right edge of the slot. The resulting BICPSA has a much larger CPBW of 39.1%, which is about 3.55 times that of the reference antenna. Finally, by placing a simple reflector underneath this BICPSA without changing its structural dimensions, one can obtain unidirectional radiation patterns with a greatly increased gain of 7.6 dBic, but with only a slightly decreased CPBW of 34.3%.