  We prove that a signed graph admits a nowhere-zero $8$-flow provided that it
is flow-admissible and the underlying graph admits a nowhere-zero $4$-flow.
When combined with the 4-color theorem, this implies that every flow-admissible
bridgeless planar signed graph admits a nowhere-zero $8$-flow. Our result
improves and generalizes previous results of Li et al. (European J. Combin. 108
(2023), 103627), which state that every flow-admissible signed
$3$-edge-colorable cubic graph admits a nowhere-zero $10$-flow, and that every
flow-admissible signed hamiltonian graph admits a nowhere-zero $8$-flow.
