The description of the main steps of the method for determination ofthe coordinates of the extremumsof non-stationary periodic signals is given. This method is based on multi-start optimization using the wavelet transform. The main steps of the base form of multi-start optimization methodwith using the wavelet transform are given. The results of investigation of noise stability and error for the search of extremumsof asymmetric and multi-modal test functions for such method are given. The main stepsof extremumsearch by such method in new method for determination ofthe coordinates of the extremum of non-stationary periodic signals are implemented.This method is implemented for automated electrocardiograms(ECG)diagnostic systems in tele-medicine. This method allowed us to determine characteristic fragments coordinates for electrocardiogram.The procedure for esti-mation of the characteristic fragmentscoordinatesand intervals between them is based on this multi-start optimization method with using the wavelet transform. The main steps of thisprocedure are described. The error inestimatingtheduration of theintervalsbetween ECG characteristic fragmentswas estimated and the noise immunity of such estimation with increasing the noise level was evaluated. The relative error in estimationofthe intervalsduration between characteristic fragments was less than 4% in the case of the signal-to-noise ratio in amplitude up to 10. These results allowrecommendingthe developed method for implementationin in-formation technologies for automated decision support systems, including telemedicine,in condition ofincreasing noise level in ECG signals. Forfurther research,it is planned to develop a methodology for estimationthe remaining parameters of characteristic fragments and complexes in ECG, reducing the edge effects during the estimation of the extremums coordinates.