Pardon?

I knew that an outgoing US President had the power to pardon convicted criminals - I remember reading a thriller (was it Grisham?) based on that very theme - but I didn't realise that a President always had that power throughout his term.  It's come to light because Trump has recently come under fire for pardoning a sheriff mate of his who was convicted of what was seen as a racist offence. What's that old saying - "It's not what you know..."?