The Millimeter-Wave Bolometric Interferometer (MBI) is designed for sensitive measurements of the polarization of the cosmic microwave background (CMB). MBI combines the differencing capabilities of an interferometer with the high sensitivity of bolometers at millimeter wavelengths. It views the sky directly through corrugated horn antennas with low sidelobes and nearly symmetric beam patterns to avoid spurious instrumental polarization from reflective optics. The design of the first version of the instrument with four 7-degree-FOV corrugated horns (MBI-4) is discussed. The MBI-4 optical band is defined by filters with a central frequency of 90 GHz. The set of baselines determined by the antenna separation makes the instrument sensitive to CMB polarization fluctuations over the multipole range l= 150-270. In MBI-4, the signals from antennas are combined with a Fizeau beam combiner and interference fringes are detected by an array of spider-web bolometers with NTD germanium thermistors. In order to separate the visibility signals from the total power detected by each bolometer, the phase of the signal from each antenna is modulated by a ferrite-based waveguide phase shifter. Observations are planned from the Pine Bluff Observatory outside Madison, WI.