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The THz pulse of a few picosecond durations have been generated and detected via optical rectification and electro-optic effect within the same ZnTe crystal. An unbalanced single-shot detection scheme was performed to characterize the signal. As a result, a multicycle signal was obtained, in which two-photon absorption and other associated nonlinear effects were reportedly negligible. The experimental set-up is compact, economical, easy to build and has the added simplicity of facilitating an independent analysis of the horizontal or vertical polarization arm of the THz-modulated chirped probe beam. This work finds a useful application in integrated THz devices, narrow-band THz phonon spectroscopy and spectroscopic investigation of fast-occurring processes.