  We use inelastic neutron scattering (INS) to study the spin excitations in
partially detwinned NaFe$_{0.985}$Co$_{0.015}$As which has coexisting static
antiferromagnetic (AF) order and superconductivity ($T_c=15$ K, $T_N=30$ K). In
previous INS work on a twinned sample, spin excitations form a dispersive sharp
resonance near $E_{r1}=3.25$ meV and a broad dispersionless mode at $E_{r1}=6$
meV at the AF ordering wave vector ${\bf Q}_{\rm AF}={\bf Q}_1=(1,0)$ and its
twinned domain ${\bf Q}_2=(0,1)$. For partially detwinned
NaFe$_{0.985}$Co$_{0.015}$As with the static AF order mostly occurring at ${\bf
Q}_{\rm AF}=(1,0)$, we still find a double resonance at both wave vectors with
similar intensity. Since ${\bf Q}_1=(1,0)$ characterizes the explicit breaking
of the spin rotational symmetry associated with the AF order, these results
indicate that the double resonance cannot be due to the static and fluctuating
AF orders, but originate from the superconducting gap anisotropy.
