A cutting tap that has an elongate tap body with a fluted section at the axial forward end thereof wherein the fluted section includes a chamfered fluted section and a finishing fluted section. Each cutting thread in the chamfered fluted section has a cutting face disposed at a cutting face angle that becomes more negative the more axially rearward the cutting thread is from the axial forward end of the chamfered fluted section. Each cutting thread in the finishing fluted section has a cutting face disposed at a finishing cutting face angle that is essentially equal. The finishing cutting face angle is more negative than the cutting face angle for the cutting thread at the axial rearward termination of the chamfered fluted section.