As there is tremendous increase in the number of active users in wireless communication there occurs a scarcity of spectrum in the available frequency spectrum. As the frequency spectrum available to us is limited so we have to utilize the available frequency spectrum in such an efficient way so that all the user can access the spectrum efficiently. To utilize the unused frequency spectrum concept of white space has been introduced. White Spaces (WS) are vacant frequencies made available for unlicensed use at locations where spectrum is not being used by another individual, such as Wi-Fi, Bluetooth, etc. In this paper, Min-Max algorithm is used for channel allocation. The Min-Max algorithm allocate channel in the available vacant space by calculating the phase, magnitude and probability of the vacant channels. Based on this results availability of vacant channel can be determined. Graphs of various parameters like power, snr will be plotted. Based on these results availability of vacant channels can be determined and using this information data is transmitting on the available channel. This paper proposes an optimal technique for the identification of vacant spaces in the unlicensed ISM (2.4-2.43Ghz) and transmit data on the detected vacant space without inference with the primary user.