In this first paper of a series we develop a new technique to analyze clusters of galaxies observed during the ROSAT All-Sky Survey (RASS). We call this method the Steepness Ratio Technique (SRT). The SRT uses the convolution between the real RASS point-spread function and the cluster emission profile assumed to be a beta-model with the beta parameter fixed to the value of 2/3. From the convolved source emission profile the SRT extracts total flux and extension (i.e., core radius) for each

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... er. Using the Steepness Ratio (SR) and a control sample of RASS pointlike sources we are able to assign to each RASS source a model-independent probability of extension. Potential biases arising from the hypotheses of a beta-model emission profile and from a fixed beta value are quantified. Tests with control samples of optically identified sources extracted from both the ROSAT survey database and from the ROSAT-PSPC pointed observations archive are performed to check the SRT output. We find that the source properties derived using the SRT on RASS data are consistent with those determined from ROSAT-PSPC pointed observations.