In this paper, the generalized likelihood ratio test-linear quadratic (GLRT-LQ) has been extended to the multiple-input multiple-output (MIMO) case where all transmit-receive subarrays are considered jointly as a system such that only one detection threshold is used. The GLRT-LQ detector has been derived based on the spherically invariant random vector (SIRV) model and is constant false alarm rate (CFAR) with respect to the clutter power fluctuations (also known as the texture). The new MIMO detector is then shown to be texture-CFAR as well. The theoretical performance of this new detector is first analytically derived and then validated using Monte Carlo simulations. Its detection performance is then compared to that of the well-known Optimum Gaussian Detector (OGD) under Gaussian and non-Gaussian clutter. Next, the adaptive version of the detector is investigated. The covariance matrix is estimated using the Fixed Point (FP) algorithm which enables the detector to remain texture- and matrix-CFAR. The effects of the estimation of the covariance matrix on the detection performance are also investigated.