  The origin of the string conformal anomaly is studied in detail. We use a
reformulated string Lagrangian which allows to consider the string tension
$T_{0}$ as a small perturbation. The expansion parameter is the worldsheet
speed of light c, which is proportional to $T_{0}$ . We examine carefully the
interplay between a null (tensionless) string and a tensionful string which
includes orders $ c^{2} $ and higher. The conformal algebra generated by the
constraints is considered. At the quantum level the normal ordering provides a
central charge proportional to $ c^{2} $. Thus it is clear that quantum null
strings respect conformal invariance and it is the string tension which
generates the conformal anomaly.
