Below-average precipitation and above-average air temperature are important factors in the occurrence and intensity of drought. In the context of global climate change, air temperature increase, as a key climatological parameter, has to be considered when calculating the drought index. We introduce a new method of drought analysis, relying on standardized values of precipitation and mean air temperatures for a certain period. The standardized value is calculated by subtracting the average value for each period from each measured value and dividing the obtained value by the standard deviation of the sample. Next, the New Drought Index (NDI) is calculated by subtracting the standardized temperature value from the standardized precipitation value. NDI values were determined for the monthly and annual precipitation time series and mean monthly and annual air temperatures measured at the stations Split-Marjan and Zagreb-Grič between 1948 and 2020. The NDI indicates that the risk of drought has intensified significantly in recent decades, which may be related to the effect of global warming.