The article introduces a new family of self-avoiding walks on the Sierpinski gasket by using a method called the 'erasing-larger-loops-first' approach. This method connects the loop-erased random walk and a self-avoiding walk with similar behaviors. The researchers prove the existence of a scaling limit for these walks and find that the path properties vary continuously with a parameter. The limit process is almost surely self-avoiding, and the path Hausdorff dimension is greater than 1.