Yes, a private company can issue unsecured debenture under section 81 of the Companies Act, 1956 read with Unlisted Public Companies(Preferential Allotment) Rules, 2003.
However the provision of section 81 of the Companies Act, 1956 read with Unlisted Public Companies(Preferential Allotment) Rules, 2003 will not apply, but if you issue debentures you should follow as good corporate practice.
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