Purpose: Abutted scatter energy windows used for a triple energy window (TEW) method may provide wrong estimation of scatter. This study is to propose an extended TEW (ETEW) method, which doesn't require abutted scatter energy windows and overcomes the shortcomings of TEW method. Materials & Methods: The ETEW is a modification of the TEW which corrects for scatter by using abutted scatter rejection windows, which can overestimate or underestimate scatter. The ETEW is compared to the TEW using Monte Carlo simulated data for point sources as well as hot and cold spheres in a cylindrical water phantom. Various main energy window widths (10 %, 15 % and 20 %) were simulated. Both TEW and ETEW improved image contrast, % recovery coefficients and normalized standard deviation. Results: Both of TEW and ETEW improved image contrast and % recovery coefficients. Estimated scatter components by the TEW were not proportional to the true scatter components over the main energy windows when ones of 10 %, 15 %, and 20 % were simulated. The ETEW linearly estimated scatter components over the width of the main energy windows. Conclusion: We extended the TEW method into the method which could linearly estimate scatter components over the main energy windows.(Korean J Nucl Med 39(3):163-173, 2005)