  The $^{22}$Ne(p,$\gamma$)$^{23}$Na reaction is included in the neon-sodium
cycle of hydrogen burning. A number of narrow resonances in the Gamow window
dominates the thermonuclear reaction rate. Several resonance strengths are only
poorly known. As a result, the $^{22}$Ne(p,$\gamma$)$^{23}$Na thermonuclear
reaction rate is the most uncertain rate of the cycle. Here, a new experimental
study of the strengths of the resonances at 436, 479, 639, 661, and 1279 keV
proton beam energy is reported. The data have been obtained using a tantalum
target implanted with $^{22}$Ne. The strengths $\omega\gamma$ of the resonances
at 436, 639, and 661 keV have been determined with a relative approach, using
the 479 and 1279 keV resonances for normalization. Subsequently, the ratio of
resonance strengths of the 479 and 1279 keV resonances was determined,
improving the precision of these two standards. The new data are consistent
with, but more precise than, the literature with the exception of the resonance
at 661 keV, which is found to be less intense by one order of magnitude. In
addition, improved branching ratios have been determined for the gamma decay of
the resonances at 436, 479, and 639 keV.
