  A discretisation method with the $H_{\rm div}$ inner product for the electric
field integral equation~(EFIE) is proposed. The EFIE with the conventional
Galerkin discretisation shows bad accuracy for problems with a small frequency,
a problem known as the low-frequency breakdown. The discretisation method
proposed in this paper utilises the $H_{\rm div}$ scalar product with a scalar
coefficient for the Galerkin discretisation and overcomes the low-frequency
problem with an appropriately chosen coefficient. As regards the
preconditioning, we find that a naive use of the widely-used Calderon
preconditioning is not efficient for reducing the computational time with the
new discretisation. We therefore propose a new preconditioning which can
accelerate the computation successfully. The efficiency of the proposed
discretisation and preconditioning is verified through some numerical examples.
