Context :

Aims : J , H , and K ^ { { } ^ { \prime } } images obtained from the near-infrared imager CFHTIR on the Canada-France-Hawaii Telescope are used to derive the morphological parameters of the red giant branch ( RGB ) in the near-infrared color-magnitude diagrams for 12 metal-poor globular clusters in the Galactic bulge direction .
Using the compiled data set of the RGB parameters for the observed 12 clusters , in addition to the previously studied 5 clusters , we discuss the properties of the RGB morphology for the clusters and compare them with the calibration relations for the metal-rich bulge clusters and the metal-poor halo clusters .

Methods : The photometric RGB shape indices such as colors at fixed magnitudes of M _ { K } = M _ { H } = ( -5.5 , -5 , -4 , and -3 ) , magnitudes at fixed colors of ( J - K ) _ { o } = ( J - H ) _ { o } = 0.7 , and the RGB slope are measured from the fiducial normal points defined in the near-infrared color-magnitude diagrams for each cluster .
The magnitudes of RGB bump and tip are also estimated from the differential and cumulative luminosity functions of the selected RGB stars .
The derived RGB parameters have been used to examine the overall behaviors of the RGB morphology as a function of cluster metallicity .

Results : The correlations between the near-infrared photometric RGB shape indices and the cluster metallicity for the programme clusters compare favorably with the previous observational calibration relations for metal-rich clusters in the Galactic bulge and the metal-poor halo clusters .
The observed near-infrared magnitudes of the RGB bump and tip for the investigated clusters are also in accordance with the previous calibration relations for the Galactic bulge clusters .

Conclusions :