Is ovulation required in order to have normal menstruation cycles?

Yes: Yes, ovulation is necesarily.

Usually yes: The hormone Progesterone is produced after ovulation by the corpus luteum cyst of the ovary. If there is no pregnancy the corpus lutem will die off after 12-14 days. Progesterone changes the lining of the uterus and when the level falls it triggers the menses. Sometimes menses will occur even without Progesterone but are usually not in a regular pattern and bleeding can last longer (8-12 days).