The notochord is a flexible rod found in the embryos of all chordates, and is replaced later in life by the vertebral column and the main axial support of the body. If the animal you are referring to is an adult and lacking a "true notochord", it is still a chordate because the notochord has simply transformed into other parts of the body. However, if it is still an embryo and STILL has no notochord, it is not a true chordate.