CPT clocks are very attractive for their miniaturization potentiality. Nevertheless, two main effects limit today their performance: the optical pumping associated with circularly polarized lasers and the line broadening due to saturation effects. We propose to overcome these limitations by the use of orthogonal linear laser polarizations and a pulsed interrogation sequence. The optimization of the time sequence leading to the best characteristics (contrast, linewidth) of the dark resonance is discussed. Very preliminary measurements of the frequency stability demonstrate an interesting performance of 3.5 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-12</sup> tau <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-frac12</sub>
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