The relative transfer function (RTF), i.e. the ratio of acoustic transfer functions between two sensors, can be used for sound source localization / beamforming based on a microphone array. The RTF is usually defined with respect to a unique reference sensor. Choosing the reference sensor may be a difficult task, especially for dynamic acoustic environment and setup. In this paper we propose to use a locally normalized RTF, in short local-RTF, as an acoustic feature to characterize the source direction. Local-RTF takes a neighbor sensor as the reference channel for a given sensor. The estimated local-RTF vector can thus avoid the bad effects of a noisy unique reference and have smaller estimation error than conventional RTF estimators. We propose two estimators for the local-RTF and concatenate the values across sensors and frequencies to form a high-dimensional vector which is utilized for source localization. Experiments with real-world signals show the interest of this approach.