Context: In 6 years of operation, INTEGRAL/ISGRI revealed more than 500 sources. Many of these sources are variable. Taking into account that nearly half of INTEGRAL/ISGRI sources are new and many of them are still unidentified, the variability properties of the sources can serve as additional parameters that may help to classify and identify the unknown sources. Aims: In order to study the variability properties of the sources detected by INTEGRAL/ISGRI we develop a method to quantify the variability of a source. We describe here our techniques and compile a catalog of the sources that fit our criteria of variability. Methods: We use the natural time binning of INTEGRAL observations called Science Window ($approx 2000$ seconds) and test the hypothesis that the detected sources are constant using a $chi^2$ all-sky map in three energy bands (20-40, 40-100, 100-200 keV). We calculate an intrinsic variance of the flux in individual pixels and use it to define the fractional variability of a source. The method is sensitive to the source variability on time scales of one Science Window and higher. We concentrate only on the sources which were already reported to be detected by INTEGRAL. Results: We present a catalog of 202 sources which are found to be significantly variable. For the catalog sources we give the measure of variability and fluxes with corresponding errors in 20-40, 40-100, 100-200 keV energy bands, and we present some statistics about the population of variable sources. The description of the physical properties of the variable sources will be given in a forthcoming paper.
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