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We consider linear time-invariant multiple-input multiple-output systems that are controllable and observable, where each output component is saturated. We demonstrate by constructive design that such systems can be globally asymptotically stabilized by output feedback without further restrictions. This result is an extension of a previous result by Kreisselmeier for single-input single-output systems. The control strategy consists of driving the components of the output vector out of saturation one by one, to identify the state of the system. Deadbeat control is then applied to drive the state to the origin.