Among the methods that have been proposed for a Multiple-Input Multiple-Output (MIMO) receiver, the V-BLAST algorithm provides a good compromise between transmission rate, achievable diversity, and decoding complexity. In this paper, we derive a new adaptive V-BLAST type equalization scheme for fast time varying, flat fading MIMO channels. The proposed equalizer stems from the Cholesky factorization of MIMO system's output data autocorrelation matrix and the equalizer's filters are updated in time using numerically robust unitary Givens rotations. The new square-root algorithm exhibits identical performance to a recently proposed V-BLAST adaptive algorithm, offering at the same time substantially reduced computational complexity. Moreover, as expected due to its squareroot form and verified by simulations, the algorithm exhibits particularly favourable numerical behaviour.