  Birds have a remarkable ability to obtain navigational information from the
Earth's magnetic field. The primary detection mechanism of this compass sense
is uncertain but appears to involve the quantum spin dynamics of radical pairs
formed transiently in cryptochrome proteins. We propose here a new version of
the current model in which spin-selective recombination of the radical pair is
not essential. One of the two radicals is imagined to react with a paramagnetic
scavenger via spin-selective electron transfer. By means of simulations of the
spin dynamics of cryptochrome-inspired radical pairs, we show that the new
scheme offers two clear and important benefits. The sensitivity to a 50 {\mu}T
magnetic field is greatly enhanced and, unlike the current model, the radicals
can be more than 2 nm apart in the magnetoreceptor protein. The latter means
that animal cryptochromes that have a tetrad (rather than a triad) of
tryptophan electron donors can still be expected to be viable as magnetic
compass sensors. Lifting the restriction on the rate of the spin-selective
recombination reaction also means that the detrimental effects of inter-radical
exchange and dipolar interactions can be minimised by placing the radicals much
further apart than in the current model.
