Cal. Sts. & High. Code § 5227

Nothing in this act contained shall prohibit the legislative body, within said one-year period referred to in Section 5222 hereof, from commencing and carrying on new proceedings for the construction of a portion of the improvement so protested against if it finds, by the affirmative vote of four-fifths of its members, that the owners of a majority of the property within the area of the assessment district to be established under said new proceedings are in favor of going forward with said portion of the improvement.