Gloria,
This happens to a lot of people for different reasons. One thing that has been researched pretty extensively is called the "Dawn Phenomenon," and makes your blood sugars shoot up around 4 am due to hormones released by the body to prepare for the start of the day. Definitely look this up and see if it helps.
If you take shots, your insulin could be wearing off before you get up in the morning. If you are on a pump, maybe you should rework your basal rates.
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