I don't know if it's normal, but mine seems to be much higher during those times, especially when I first wake up in the morning. Mine is at it's lowest during the evening. What medication(if any) are you taking.
I have taken a low dose of Maxide for quite a few years.1/2 of a 25mg one day and only 1/4 of one the next. For the past week I am taking 1/2 each day and the pressure is now fine during the night.The only problem I have with it is that it is very drying.It has gone down from 148/90 to 116/70.
I have also noticed a morning phenomenon where my BP goes up. This is a time when adrenaline levels are typically highest and they fall off over the course of the day. Perhaps one reason why heart attacks are more common in the early hours of the day.
Sometmes if i wake up in the night (especially if i have gone to sleep 'stressed') my BP can be way up. Towards the end of the day it often drops down nice and low. If only it would stay that way all the time.