It is very important to capture distant-talking speech with high quality for teleconferencing systems or voice-controlled systems. For this purpose, microphone array steering and Fourier spectral subtraction, for example, are ideal candidates. A combination technique using both microphone array steering and Fourier spectral subtraction has also been proposed to improve performance. However, it is difficult for the conventional approach to reduce non-stationary noise, although it is easy to robustly reduce stationary noise. To cope with this problem, we propose a new combination technique with microphone array steering and Fourier / wavelet spectral subtraction. Wavelet spectral subtraction promises to effectively reduce non-stationary noise, because the wavelet transform admits a variable time-frequency resolution on each frequency band. As a result of an evaluation experiment in a real room, we confirmed that the proposed combination technique provides better performance of the ASR (Automatic Speech Recognition) and NRR (Noise Reduction Rate) than the conventional combination technique.