The series of H- resonances of P-1(o) symmetry predicted to converge e
xponentially to all thresholds has been investigated below the H(n=2)
threshold. It is shown that the series will be terminated already afte
r the third resonance when the relativistic and radiative splitting of
the H(n=2) states is considered. Resonance parameters of this third r
esonance have been calculated with highly correlated wave functions. T
he resonance is predicted to be situated 19 mu eV below H(2p(1/2)) wit
h a width of 0.06 mu eV. Accurate resonance parameters are also given
for the first two resonances and the photoabsorption cross section is
calculated for the threshold region.