Looking for a template to provide an improved auditing style?

In the past our auditing schedule was department based and had been sufficient for many years. However over recent times the schedule was challenged and found to be inadequate in covering all aspects of the accreditation. Therefore the schedule was updated to correspond with the six sections of the accreditation. However this seemed to be more challenging for the auditors and in one instance where the BRC checklist had been used to challenge the procedures, it was stated as bad practice by an external auditor.

So what is the way around it or has anyone got a template to provide an improved auditing style?

One of practices I have referred is ASQ Guide: The Process Auditing and Techniques. In that guide, they call auditing by SOIs of BRC an elementary audit. They suggest to system audit. 

You can find it on ASQ website if get interested.