The recovery of blocks of missing values in regular time series has been addressed by model-based techniques. Such techniques are not suitable to recover blocks of missing values in irregular time series and restore peaks and valleys. We propose REBOM (REcovery of BlOcks of Missing values): a new technique that reconstructs shape, amplitude and width of missing peaks and valleys in irregular time series. REBOM successfully reconstructs peaks and valleys by iteratively considering the time series itself and its correlation to multiple other time series. We provide an iterative algorithm to recover blocks of missing values and analytically investigate its monotonicity and termination. Our experiments with synthetic and real world hydrological data confirm that for the recovery of blocks of missing values in irregular time series REBOM is more accurate than existing methods.