The frequency of the transition between the 3dσ G K 1Σg + (v = 1, N = 1) state of H 2 and the n = 56p ( N = 1, S = 0) Rydberg state belonging to a series converging to the X+ 2Σg + (v+ = 0, N+ = 1) ground state of ortho H2+ has been measured with an accuracy of 1.2 MHz using a narrow-band pulsed near-infrared (NIR) laser. Systematic errors originating from ac and dc Stark shifts, from pressure shifts and from the frequency shift and chirp accompanying the generation of the NIR laser pulses were quantified. By combining this frequency with the binding energy of the 56p (N = 1, S = 0) Rydberg state, the ionisation energy of the G K 1Σg + (v = 1, N = 1) state of ortho H2 was determined to be 379855188.3(12) MHz [12670.60522(4) cm-1]. This new result represents the first step towards the determination of the ionisation and dissociation energies of molecular hydrogen at a ν/Δν level of accuracy beyond 10 10. Using the current value of the ionisation energy of ortho H 2 [124357.23797(36) cm-1, from Liu et al. [J. Chem. Phys. 130, 174306 (2009)] and the frequency interval between the N = 1 and N = 0 rotational levels of the X (v = 0) ground state of H2 [118.48684(10) cm-1, from Jennings et al. [J. Mol. Spectrosc. 126, 19 (1987)], the term value of the G K 1Σg + (v = 1, N = 1) state was determined to be 111805.1196(4) cm-1. © 2013 Taylor & Francis.