We have investigated the resistive superconducting transition of beta(
H)-(ET)2I3 crystals in which the two inner carbon atoms, in the center
of the ET molecule, have been substituted with C-13 isotopes. We stab
ilised the beta(H) State of (ET)213 at low temperature via the appropr
iate cooling procedure in a He gas pressure apparatus (''Orsay process
''). The superconducting transition of C-13 substituted samples was fo
und to be T(c) = 7.80+/-0.05K (at midpoint ), namely 0.20K lower than
that of standard C-12 samples (T(c) = 8.0+/-0.1K). We have taken care
that both types of samples were measured in the same conditions and th
at rho(T) data were free from cracks which can broaden the superconduc
ting transition. This large and regular isotope shift of T(c) is in co
ntrast with most of the previous results in organic superconductors an
d suggests the existence of a superconductivity mechanism mediated by
the coupling of electrons with the intramolecular phonon modes.