Is ovulation required in order to have normal menstruation cycles?

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).