A new transaural system, referred to as the ``stereo dipole'' reproduction system (hereafter the SD system), using a closely spaced pair of loudspeakers in front of a listener, has been introduced recently. In this paper, the deconvolution techniques used in the SD system, in which a 2x2 matrix of digital filters is used to compensate for the response of the loudspeakers and to create virtual sound sources, are dealt with. The deconvolution method is based on the analysis of a matrix of exact least-squares inverse filters. Two kinds of design techniques are developed. One is a very fast FFT-based deconvolution method; the other is a time-domain counterpart to the FFT method. The well-known principles of least-squares optimization and regularization are introduced in both the design methods. The relationships between the characteristics of the deconvolution filters and loudspeaker arrangement are investigated. In particular,the theoretical analysis is concerned with the locations of poles and zeros and the required dynamic range of the filter. Computer simulation reveals that the SD system offers the robustness of the sound image and a wide range of equalization area relative to the ordinary loudspeaker arrangement system. Finally, the subjective effects of the filter characteristic are also discussed.