  In two dimensions, it is well known that the scale invariance can be
considered as conformal invariance. However, there is no solid proof of this
equivalence in four or higher dimensions. We address this issue in the context
of 4d $\mathcal{N}=1$ SUSY theories. The SUSY version of dilatation current for
theories without conserved $R$ symmetry is constructed through the
FZ-multiplet. We discover that the scale-invariant SUSY theory is also
conformal when the real superfield in the dilatation current multiplet is
conserved. Otherwise, it is only scale-invariant, despite of the transformation
of improvement.
