Monitor's "on" indicator blinks while computer is off

The indicator is on the power button. Of course if I turn off my computer, I could also turn off my monitor so it does not blink, but is there a way to just let it not blink while it gets no signal? My old monitor did this (Samsung 19") and my new one (Samsung 24") does not. It’s really distracting when it blinks at night while I’m trying to sleep.