To expand on the other good answers here. It shouldn't be a rule but...
Is there a certain rule that manager should have better salary than
all of his subordinates?
This rule/myth originates from managers but is believed by a significant number of people in all positions. Even if it isn't a good rule you should be aware that it exists in parts of the real world. Adherents to the rule are usually resolute and are not ready to be persuaded that anything else would be fair or even viable.
Therefore, if you meet someone who believes in this rule you should think about how you can work around it rather than trying to change their minds.
Sometimes the rule will be believed by a manager (work around them not against them) but sometimes it will be intrinsic to an organisation. For example, the NHS has a pay banding structure predicated on the idea that managers are paid more than their employees*. If you want sizeable long term pay rises and also want to work for the NHS then you should try to obtain a role and responsibilities that can have the word "manager" attached to them.
* with the sole exception of doctors (1% of NHS employees). Doctors are valued differently but I don't want to get into details too much as the specifics aren't relevant to the question at hand.