The Stegeman Building was constructed in 1879 by its namesake, Frederick W. Stegeman. It was originally built with two stories and the third-level, visible in the above photo, was added in 1890.
Houston has a complete disregard of historical significance and a knack for bulldozing. However, there are still some extant gems sprinkled throughout the city and this corner is one of them.
While the 1890 third-floor of the Stegeman Building has been removed, most of this corner is still standing.