The recently proposed `Sub-Band DFT' (SB-DFT) method , ,  has two requirements to be fully adaptive. The first requirement is to select the frequency bands containing most of the signal's energy in the successive stages of the algorithm. The second requirement is to find the index of the first DFT coefficient in the sub-band to be analyzed. A method proposed for the band selection previously is both improved and simplified. The problem of the index calculation is solved in this work using a new algorithm. The fully adaptive SB-DFT works for any arbitrary number and type of decompositions (such as low-high-low-low-high, etc.). It is found to be faster than other methods that can be used in partial band DFT analysis. With this last result, many fields of application will be opened for the SB-DFT method.