Hewlett-Packard got it at least half-right in choosing its new leaders. The tech company’s decision to appoint ex-SAP boss Leo Apotheker as chief executive officer raises questions. He was forced out at SAP , and may have a tough time firing up HP’s troops. On the other hand, HP’s decision to split the chairman and CEO roles is solid.

Apotheker has a fitting background. He spent more than 20 years at SAP. So he understands the marketplace for enterprise software, which is a big and growing part of HP. His international background should also be useful in running a multinational business. Furthermore, his past presumably fires him up to take on old rivals such as Oracle – which hired his predecessor Mark Hurd – and new ones such as SAP itself.

Yet the twilight of his career at SAP raises questions. He was appointed co-chief executive in 2008, and had sole hands on the reins for less than a year before his contract wasn’t renewed. His attempt to raise prices, in the midst of the recession, set off a customer revolt. And his decision to lay off thousands of SAP employees may have been correct, but it won’t endear him to HP’s employees.

Many of HP’s rank-and-file feel disgruntled over the company’s past leadership and Hurd’s chain-sawing through the ranks. Apotheker could win these employees over, but he may be greeted with skepticism. Furthermore, top execs that lost the race to Apotheker may depart if they have a better shot at leading a company elsewhere.

The board’s decision to split the roles of chairman and CEO is unquestionably a good one. Separating the roles increases accountability at the board level, and allows Apotheker to concentrate on running HP day-to-day. The new chairman, Ray Lane, has both depth and breadth of experience in the tech industry from his past as an Oracle executive and as a venture capitalist. His strategic insight should be useful. And Apotheker will need all the help he can get.