  We introduce new color indices $cn^\prime_{\rm JWL}$ (= $Ca_{\rm CTIO} -
Ca_{\rm JWL}$) and $ch_{\rm JWL}$ [=$(JWL43 - b) - (b-y)$], accurate
photometric measures of the CN band at $\lambda$3883 and the CH G band,
respectively, in the study of the multiple populations (MPs) in globular
clusters (GCs). Our photometric CN--CH relation for a large number of red-giant
branch (RGB) in M5 shows that the evolutions of the CN and CH between the CN-w
and CN-s populations are not continuous. Armed with our new color indices, we
investigate the MPs of NGC 6723, finding the RGB populational number ratio of
$n$(CN-w):$n$(CN-s) $\approx$ 35.5:64.5 ($\pm$2.8) with no radial gradient.
Similar to other normal GCs with MPs, the helium abundance of the CN-s
population inferred from the RGB bump magnitude is slightly enhanced by $\Delta
Y$ = 0.012 $\pm$ 0.012. Our $cn_{\rm JWL}$ and $cn^\prime_{\rm JWL}$
color-magnitude diagrams clearly show the discrete double AGB populations in
NGC 6723, whose bright AGB populational number ratio is in marginally agreement
with that of the RGB stars within the statistical errors. Finally, our
synthetic $cn_{\rm JWL}$ index is in good agreement with observations, except
for the CN-w asymptotic giant branch (AGB). To mitigate the discrepancy in the
CN-w AGB may require a mild nitrogen enhancement and/or a large decrement in
the $^{12}$C/$^{13}$C ratio with respect to the bright RGB.
