While there are older writing systems like cuneiform and hieroglyphs, they are not continuously written. They evolved and changed significantly over time, leading to different forms and styles.
Ancient Egyptian, however, has been continuously written from its earliest known appearance in the 32nd century BCE (around 3100 BCE) until its modern form, Coptic, which was written in the early 18th century. This makes it the oldest language in the world with an unbroken chain of writing spanning over 5,000 years.