The city superintendent of schools shall, at such times and in such manner as directed by the city board of education, under the rules and regulations promulgated by the State Superintendent of Education, prepare his payroll or payrolls for the payment of teachers, employees, bills and other items authorized by the city board of education. No public funds must be paid out by the city treasurer except on an order signed by the chairman of the city board of education, accompanied by a certificate of the city superintendent of schools that the payroll or order is correct, due and unpaid.