With over 5 years of GOLF data having some 90% continuity, a new attempt has been made to search for possible solar g modes. Statistical methods are used, based on the minimum of assumptions regarding the solar physics; namely that mode line-widths are small compared with the inverse of the observing time, and that modes are sought in the frequency interval 150 to 400 mu Hz. A number of simulations are carried out in order to understand the expected behaviour of a system consisting principally of a solar noise continuum overlaid with some weak sharp resonances. The method adopted is based on the FFT analysis of a time series with zero-padding by a factor of 5. One prominent resonance at 284.666 mu Hz coincides with a previous tentative assignment as one member of an n=1, l=1, p-mode multiplet. Components of two multiplets, previously tentatively identified as possible g-mode candidates from the GOLF data in 1998, continue to be found, although their statistical significance is shown to be insufficient, within the present assumption regarding the nature of the signal. An upper limit to the amplitude of any g mode present is calculated using two different statistical approaches, according to either the assumed absence (H0 hypothesis) or the assumed presence (H1 hypothesis) of a signal. The former yields a slightly lower limit of around 6 mm/s.