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We present the results from the Optical Gravitational Lensing Experiment II (OGLE‐II) survey (1996–2000) towards the Large Magellanic Cloud (LMC), which has the aim of detecting the microlensing phenomena caused by dark matter compact objects in the Galactic halo [massive compact halo objects (MACHOs)].  We use high‐resolution  Hubble Space Telescope  images of the OGLE fields and derive the correction for the number of monitored stars in each field. This also yields blending distributions which we use in ‘catalogue‐level’ Monte Carlo simulations of the microlensing events in order to calculate the detection efficiency of the events.  We detect two candidates for microlensing events in the All Stars Sample, which translates into an optical depth of  0.43 ± 0.33 × 10 −7  . If both events were due to MACHO, the fraction of mass of compact dark matter objects in the Galactic halo would be  8 ± 6  per cent. This optical depth, however, along with the characteristics of the events seems to be consistent with the self‐lensing scenario, i.e. self‐lensing alone is sufficient to explain the observed microlensing signal. Our results indicate the non‐detection of MACHOs lensing towards the LMC with an upper limit on their abundance in the Galactic halo of 19 per cent for   M = 0.4 M ⊙   and 10 per cent for masses between 0.01 and  0.2 M ⊙  .

The OGLE view of microlensing towards the Magellanic Clouds – I. A trickle of events in the OGLE‐II LMC data ★