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We report the detection of the Lyman continuum (LyC) radiation of the compact star-forming galaxy (SFG) J1154+2443 observed with the Cosmic Origins Spectrograph (COS) onboard the Hubble Space Telescope. This galaxy, at a redshift of z = 0.3690, is characterized by a high emission-line flux ratio O-32 = [O III] lambda 5007/[O II] lambda 3727 = 11.5. The escape fraction of the LyC radiation f(esc)(LyC) in this galaxy is 46 per cent, the highest value found so far in low-redshift SFGs and one of the highest values found in galaxies at any redshift. The narrow double-peaked Ly alpha emission line is detected in the spectrum of J1154+2443 with a separation between the peaks V-sep of 199 km s(-1), one of the lowest known for Ly alpha-emitting galaxies, implying a high f(esc)(Ly alpha). Comparing the extinction-corrected Ly alpha/H beta flux ratio with the case B value, we find f(esc)(Ly alpha) = 98 per cent. Our observations, combined with previous detections in the literature, reveal an increase of O-32 with increasing f(esc)(LyC). We also find a tight anticorrelation between f(esc)(LyC) and V-sep. The surface brightness profile derived from the COS acquisition image reveals a bright star-forming region in the centre and an exponential disc in the outskirts with a disc scale length alpha = 1.09 kpc. J1154+2443, compared to other known low-redshift LyC leakers, is characterized by the lowest metallicity, 12+log O/H = 7.65 +/- 0.01, the lowest stellar mass M-star = 108.20 M-circle dot, a similar star formation rate SFR = 18.9 M-circle dot yr(-1), and a high specific SFR of 1.2 x 10(-7) yr(-1).