We analyze the  capacity  of Rayleigh block- fading  multiple- input  multiple-output ( MIMO )  channels  in the noncoherent setting and prove that  unitary  space-time modulation (USTM) is not  capacity - achieving  when the total number of antennas exceeds the coherence time of the  fading   channel . This situation is relevant for  MIMO  systems with  large  antenna arrays ( large - MIMO  systems). Our result settles a conjecture by Zheng & Tse (2002) in the affirmative. The  capacity - achieving   input signal, which we refer to as Beta-variate space-time modulation (BSTM), turns out to be the product of a  unitary   isotropically   distributed  random matrix, and a diagonal matrix whose nonzero entries are distributed  as the square-root of the eigenvalues of a Beta- distributed  random matrix of appropriate size. Numerical results illustrate that using BSTM instead of USTM in  large - MIMO  systems yields a rate gain as  large  as 13% for SNR values of practical interest.