  We report a new form of compensating accelerating beam generated by amplitude
modulation of the symmetric Airy beam (SAB) caustics with an exponential
apodization mask. Our numerical study manifests that the compensating beam is
with one main-lobe beam structure and can maintain the mean-intensity invariant
both in the free space and loss media. Specially, the beam inherits the
beamlets structure from the SAB and owns a novel damped oscillating propagation
property. We also conduct a comparative study of its propagation property with
that of the Airy beam theoretically. And by altering the signs of 2D masks, the
main lobe of the compensating beam can be modulated to orientate in four
different quadrants flexibly. The proposed compensating accelerating beam is
anticipated to get special applications in particle manipulation or plasmas
regions.
