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We introduce new color indices cn_JWL^′^ (=Ca_CTIO - Ca_JWL) and ch_JWL [=(JWL43 - b) - (b - y)], accurate photometric measures of the CN band at λ3883 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) ≃ 35.5:64.5 (±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 ΔY = 0.012 ± 0.012. Our cn_JWL and cn_JWL^′^ color-magnitude diagrams clearly show the discrete double asymptotic giant branch (AGB) populations in NGC 6723, whose bright AGB populational number ratio is in marginal agreement with that of the RGB stars within the statistical errors. Finally, our synthetic cn_JWL index is in good agreement with observations, except for the CN-w AGB. Mitigation of the discrepancy in the CN-w AGB may require a mild nitrogen enhancement and/or a large decrement in the ¹²C/¹³C ratio with respect to the bright RGB.