No, not always. It's normal for period blood to be brown as well as red.
Our periods are as individual as we are. Blood flow isn't exactly the same every time we have a period, especially for the first couple of years following menarche.
Menstrual flow also can look different over the course of the same period. Blood may start out bright red and turn darker red or brown toward the end of the period. Or blood may start out brown and turn red. And differences in texture, like blood clots and tissue, can happen as the uterus sheds its extra lining.
Lots of girls worry about whether their periods are normal. Although differences in menstrual flow are usually nothing to be concerned about, a doctor or nurse can always answer any questions you have. In fact, if your period lasts longer than 7 days or soaks through more than one pad or tampon every 1–2 hours, it's a good idea to talk to a doctor.