A detailed line shape analysis of 23Na nuclear magnetic resonance spectra within dense suspensions (12%vol/vol) of Laponite clay exhibits a macroscopic ordering of these charged anisotropic colloids within a nematicphase. The angular variation of the order parameter limits to 20% of the maximum amount of disorder inthese dense suspensions. By contrast, dilute Laponite suspensions (1−4% vol/vol) remain isotropic while thevariation of 23Na relaxation rates over a broad range of frequencies indicates a local ordering of the clayplatelets within microdomains of the same spatial extent than the particle diameter (300 Å).