The exact null distribution of Wilks' L VC_ criterion for testing the hypothesis , α and ρ unknown,against the alternative A ≠ H where , in a p-variate complex normal population , has been derived in a gamma series form and in an alternate series form using contour integration. Percentage points for p =2 (1) 8 for various levels of significance and various degrees of freedom have been computed but in this paper we present selected tables only.