We present a broadband single-mode bi-conical microfiber coupler (MFC) with a specifically designed transition region that effectively suppresses any higher-order modes present at the input fiber and provides efficient power splitting into the fundamental mode at the two output ports. As a practical example, single-mode 3-dB splitting operation over a broad spectral window (400 approximately 1700 nm) was demonstrated for a very thin taper waist approximately 1.5 microm) MFC made from conventional telecom optical fibers.