Unlike typical choropleth maps that use graphic symbols to represent quantitative attributes for defined regions, cartograms intentionally distort the boundaries of regions so that the size of the distorted regions is proportional to their attribute. Although an Avenue script for making cartograms is published, it has been rarely used mainly because the algorithm is time-consuming. Generating a cartogram for a map showing the 50 states of United States may require hours of computation. Moreover, it cannot handle regions that are divided into multiple polygons. This paper describes an improved algorithm for creating cartograms more efficiently. The new algorithm has been implemented in Avenue.