The bootstrap calculations of baryon magnetic moments by Dashen and Frautschi and by Barton and Dare are examined in an ${\mathrm{SU}}_{2}$ model. The pion contribution to the nucleon magnetic moment, which Dashen and Frautschi neglected, is calculated using their method, and is shown to reduce to Barton and Dare's estimate in a nonrelativistic limit. In the ${\mathrm{SU}}_{2}$ model, Dashen and Frautschi's method gives for the nucleon isoscalar and vector magnetic moments: ${\ensuremath{\mu}}_{S}=0$ and $0l{\ensuremath{\mu}}_{V}l5.7(\frac{e}{2M})$, where $M$ is the nucleon mass.