A new method for global optimization of H\"older goal functions under compact sets given by inequalities is proposed. All functions are defined only algorithmically. The method is based on performing simple Monte Carlo trials and constructing the sequences of records and the sequence of their decrements. An estimating procedure of H\"{o}lder constants is proposed. Probability estimation of exact global minimum neighborhood using H\"older constants estimates is presented. Results on some analytical and algorithmic test problems illustrate the method's performance.