SAN FRANCISCO — Late last year, Hewlett-Packard split itself into two, believing that smaller was better.

Now one of those publicly traded companies is making itself even smaller.

Hewlett Packard Enterprise said on Tuesday that it would sell its business that focuses on call centers and maintains networks for clients to the Computer Sciences Corporation in an all-stock deal that would create a new company worth roughly $9 billion.

The deal is meant to be the next step in the turnaround of the corporate descendants of Hewlett-Packard, which broke itself apart last fall after years of struggling to turn around its fortunes. The Silicon Valley icon split itself into two smaller companies: HP Enterprise, which focuses on selling hardware like servers to corporate customers, and HP Inc., which specializes in personal computers and printers.

Behind the split was the belief of Meg Whitman, the former chief executive of Hewlett-Packard and now the leader of HP Enterprise, that focus is better. It is a decidedly different path from what others in the corporate computing business are taking: Dell is in the midst of buying the data storage business EMC to create a huge giant in the field.