We present a detailed study of the internal kinematics of the Galactic Globular Cluster M 4 ( NGC 6121 ) , by deriving the radial velocities from 7250 spectra for 2771 stars distributed from the upper part of the Red Giant Branch down to the Main Sequence .
We describe new approaches to determine the wavelength solution from day-time calibrations and to determine the radial velocity drifts that can occur between calibration and science observations when observing with the GIRAFFE spectrograph at VLT .

Two techniques to determine the radial velocity are compared , after a qualitative description of their advantages with respect to other commonly used algorithm , and a new approach to remove the sky contribution from the spectra obtained with fibre-fed spectrograph and further improve the radial velocity precision is presented .
The average radial velocity of the cluster is \langle v \rangle = 71.08 \pm 0.08 km s ^ { -1 } with an average dispersion of \mu _ { v _ { c } } = 3.97 km s ^ { -1 } .
Using the same dataset and the same statistical approach of previous analyses , 20 additional binary candidates are found , for a total of 87 candidates .
A new determination of the internal radial velocity dispersion as a function of cluster distance is presented , resulting in a dispersion of 4.5 km s ^ { -1 } within 2 \arcmin from the center of cluster and steadily decreasing outward .
We statistically confirm the small amplitude of the cluster rotation , as suggested in the past by several authors .
This new analysis represents a significant improvement with respect to previous results in literature and provides a fundamental observational input for the modeling of the cluster dynamics .