We show that the earliest possible reionisation of the Universe is approximately at z \simeq 13.5 and the optical depth is \tau \simeq 0.17 
in the conventionally accepted \Lambda 
cold dark matter ( \Lambda CDM ) model with adiabatic fluctuations of a flat spectrum normalised to the cosmic microwave background .
This is consistent with the reionisation found by WMAP ( the apparently earlier reionisation epoch of the WMAP is ascribed to the adoption of the instantaneous reionisation approximation ) , i.e. , the WMAP result is realised only if reionisation of the universe takes place nearly at the maximal efficiency in the \Lambda CDM model .