Formal:
* Inflexible principles
* Unyielding ethics
* Rigorous moral code
* Implacable righteousness
* Absolute integrity
More informal:
* Ironclad ethics
* Uncompromising values
* Rock-solid principles
* Firm beliefs
* Steadfast convictions
More negative connotations:
* Dogmatism
* Moral absolutism
* Legalistic
* Fanaticism
* Puritanical
The best synonym for you will depend on the context of your writing. For example, "unbending morality" might be used to describe a person who is unwilling to compromise their principles, even in difficult situations. "Inflexible principles" might be used to describe a person who is very strict and follows rules rigidly. "Dogmatism" would suggest a person who is stubborn and unwilling to listen to other points of view.