If the bonds canceled are issued pursuant to the Improvement Bond Act of 1915 to pay the cost of any work or improvement made under the Improvement Act of 1911, the board shall reduce the principal amount of the assessments securing the bonds to the total principal amount of the unpaid and uncanceled bonds of the same issue. The reduction of assessments shall be carried out by canceling such proportion of the assessments as is necessary, and the board shall provide procedure for the cancellation in accordance with constitutional requirements. The uncanceled portion of the assessments shall be valid and collected in accordance with the terms of the statutes under which the original assessments were levied and bonds issued.