A novel non-coherent BPSK modulation and demodulation scheme is proposed to remove both slow and fast fading completely. We formulate a compound function that reflects the different characteristics of both slow and fast fading and prove that the scheme can remove fading from the function completely. The scheme is reified by a simple architecture that can remove slow and fast phase shifts completely from the received signals. It is shown by using analytical model and numerical data that the proposed scheme outperforms other ones significantly under the presence of both slow and fast fading. The analytical results also show that the proposed scheme can work well even with a small sampling rate, resulting in a wireless device with low energy consumption.