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Context. Several dynamically cold streams have been associated with certain globular clusters (GCs) based on orbital energies and angular momenta. Some of these streams are surprisingly far apart from their progenitors and one such pair is Triangulum and NGC 5824. Triangulum can be considered as a piece of NGC 5824 leading tail since the cluster's future orbit matches with the stream's track well. The existence of the leading tail for NGC 5824 is the motivation behind the search for its trailing tail. Aims. Our goal is to confirm the connection between Triangulum and NGC 5824 and seek the trailing tail of the cluster. Methods. The selection of member stars of Triangulum is made through various cuts in metallicity, proper motions (PMs), radial velocity and color-magnitude diagram (CMD). The selected members are compared in phase space to a mock stream which models the disruption of NGC 5824. We then try to detect the trailing tail of the cluster based on a modified matched-filter technique. Stars are assigned weights using their color differences from the cluster's locus in CMD. These weights are further scaled based on stars' departures from expected PMs of the model stream. Results. A total of 26 member stars for Triangulum are obtained and 16 of them are newly identified. These members are consistent with the mock stream in the phase space and their metalicity and position on the CMD are in good agreements with NGC 5824. By applying the matched-filter, a tenuous trailing tail of the cluster is detected, spanning $\sim$ 50$^\circ$ long on sky. The signature matches with the mock stream's trajectory well. Conclusions. Our results support that Triangulum stream acts as a part of the leading tail for NGC 5824. On the trailing side, we have detected a 50$^\circ$ tail extended from the cluster. The existence of both leading and trailing tails for the GC NGC 5824 is verified.