With next generation of wireless communication systems being conceptualised with new applications, smart devices and use cases which demand unprecedented levels of high data rates,spectral efficiency, reliability ,low latency andwith high energy efficiency.The Index modulated Orthogonal frequency division multiplexing (OFDM-IM) stand out as the most endearing physical layer modulation technique capable of providing greener communications. However, OFDM-IM is also very sensitive to frequency synchronization errors similar to classical OFDM and needs to be addressed on priority. In this article a novel algorithm is proposed which estimates and correctsthe introduced carrier frequency offset during transmission using the remodulated guard interval period (cyclic prefix) which is inherent to every symbol transmitted and the algorithm’s performance is compared to that of Yang’s algorithm in two variants of OFDM-IM and we show that our algorithm gives better performance and it is independent of any frequency domain IM schemes.