  In this paper, we modify our previous research carefully, and derive a new
expression of electron energy density in superhigh magnetic fields. Based on
our improved model, we re-compute the electron capture rates and the magnetic
fields' evolutionary timescales $t$ of magnetars. According to the calculated
results, the superhigh magnetic fields may evolve on timescales $\sim
(10^{6}-10^{7})$ yrs for common magnetars, and the maximum timescale of the
field decay, $t\approx 2.9507 \times 10^{6}$ yrs, corresponding to an initial
internal magnetic field $B_{\rm 0}= 3.0 \times 10^ {15}$ G and an initial inner
temperature $T_{\rm 0}= 2.6 \times 10^ {8}$ K. Motivated by the results of the
neutron star-supernova remnant(SNR) association of Zhang $\&$ Xie(2011), we
calculate the maximum $B_{\rm 0}$ of magnetar progenitors, $B_{\rm max}\sim
(2.0\times 10^{14}-2.93 \times 10^{15})$ G when $T_{\rm 0}= 2.6 \times 10^ {8}$
K. When $T_{\rm 0}\sim 2.75 \times 10^ {8}-~1.75 \times 10^ {8}$ K, the maximum
$B_{\rm 0}$ will also be in the range of $\sim 10^{14}-10^{15}$ G, not
exceeding the upper limit of magnetic field of a magnetar under our magnetar
model. We also investigate the relationship between the spin-down ages of
magnetars and the ages of their SNRs, and explain why all AXPs associated with
SNRs look older than their real ages, whereas all SGRs associated with SNRs
appear younger than they are.
