We classify the commutator preserving bijections of the unipotent radical Up(2n, F) of the Borel subgroup of the classical symplectic group of rank at least 2 over a field F such that 6F=F. Every such a bijection is shown to be the composition of a standard automorphism of Up(2n, F) and a central map. The latter is the identity modulo the centre of (2n, F).