The revised policy is intended to bring the Church into line with the Employment Equality (Religion or Belief) Regulations, which the UK has introduced in the wake of European regulations.
Michael McGrath, director of the Scottish Catholic Education Service, told The TES Scotland: "The Church is not insisting that every teacher appointed to a Catholic school is Catholic. However, we do insist on the right to ensure that every appointment is appropriate to the particular post, and this will involve the local bishop making a judgment on a teacher's suitability in terms of his or her faith background and commitment to the aims, mission, ethos and values of the Catholic school."
The Church is confident following legal advice that its new policy, approved by bishops last month, will meet the terms of the regulations - although that might not be enough to ward off a test case in the courts.
The Church says that the new regulations allow for exemptions where there is "a genuine occupational requirement" for an employee to be of a particular religion or belief if the religious ethos of an organisation demands it.
The significant change, ironically, affects non-Catholics. Until now, most (though not all) bishops did not subject them to questions about "appropriate religious belief and character".
In the future, so as not to appear to be discriminatory, that question will have to be put to all applicants and they will have to demonstrate that they are "committed to the mission of the Catholic school and qualified to understand and support our philosophy", as Mr McGrath put it.
"The differentiation will come when the local bishop makes his decision on the basis of the answer he gets," Mr McGrath said. "We recognise that Catholic schools have many non-Catholic teachers who make a very important contribution to our schools.
"But we have to be able to guarantee the rights of parents to have their children educated appropriately in accordance with their own religious beliefs."
Talks are now under way with the Scottish Executive and with directors of education to clarify the operation of the new appointments system for Catholic schools.
Mr McGrath says that schools are anxious to bring consistency to the way the system works. A handful of authorities still operate the former Strathclyde Region policy which reserved particular posts for "Catholics only", such as senior school management and those touching on sensitive faith matters in guidance, biology and religious education.
The 1980 Education (Scotland) Act, however, stipulates that all teachers not just those in reserved posts should have been granted approval by the Church.
Mr McGrath insisted: "This is not about creating 'jobs for Catholics', an impression which may be out there and which we are anxious to dispel. This is about creating a system which is fair and transparent."