The Witten index I w in the SU(2) SUSY Yang-Mills theory is calculated by use of the functional integral representation. Our result is I w = 1 which disagrees with Witten's result: I w = N for the SU( N) gauge group. The reason for the disagreement stems, seemingly, from the appearance of a continuum spectrum in the corresponding quantum mechanical problem. The principal physical conclusion of SUSY unbreaking in this theory remains intact.