In this letter we address a particular aspect of the finite size effect on ferroelectric instability: the polarization suppression under high hydrostatic pressure. We have shown that in TGS ([NH3+CH2COOH)2(NH3+CH2COO-)SO42-]) single crystals under high pressure the critical temperature TC of ferroelectric-paraelectric phase transition grows monotonically up to about 1.8 GPa. Above the critical pressure Pc >= 2.4 GPa, the ferroelectricity disappears and the coefficient gamma becomes negative for small ferroelectric regions which appear due to crystal break up.
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