It has a central core with steel brackets supporting each floor. When completed in 1977, it was one of the three such buildings in the world based on this design concept. Imposing, beautiful and unique in concept, the 30-storey aluminium and glass building Yayasan Sabah Group headquarters, the Menara Tun Mustapha is one of the most extraordinary buildings in the country.

Built with bold architectural and engineering concepts, it is a building many thoughts was not possible to construct as it was the first of its kind in this region. The building is structured as a 72-sided polygon with walls made of 2,160 special reflective glass panels that can withstand wind speed up to 272 km/hour. Suspended from the central core of the building are steel radial brackets where some 96 high-tensile steel rods are hung and hold the 30 floors of the building. This building is known to be the fourth of such high-rise "hanging" office building in the world and has been a famous landmark and tourist attraction ever since its construction in 1975.

On 31 July 2001, in conjunction with the 35th anniversary of the establishment of Yayasan Sabah, the building was named "Menara Tun Mustapha", after the late Tun Datu Haji Mustapha bin Datu Harun, a hero and patriot of the State, national and international level.