FRANKFURT/MUNICH, Dec 6 (Reuters) - German dialysis specialist Fresenius Medical Care's (FMC) Chief Executive Carla Kriwet stepped down on Monday, marking the second leadership change in as many months as parent Fresenius pushes for a faster overhaul of the struggling unit.

FMC late on Monday said Kriwet, who had taken over as CEO on Oct. 1, had decided to leave due to "strategic differences" and would be succeeded by finance chief Helen Giza.

The FMC stock was down 4.2% at 1340 GMT, at the bottom of Germany's blue-chip index, on what Credit Suisse called an "unexpected and negative" development.

"In a fundamentally sound industry, Fresenius Medical Care now needs to sharpen its focus on the operational turnaround, further drive performance improvements and focus on its core," said Michael Sen, who took over as CEO of Fresenius in October.

Sen, who is also chairman of FMC and a former executive at Siemens and E.ON, has embarked on what he calls a "top-to-bottom" review of all business activities, with a focus on profitability.

The move comes amid speculation that activist investor Elliott, which according to a source has taken a stake in Fresenius, is pushing for a breakup of the diversified healthcare group.

"We expect that at least two business areas will be put under review and that a decision will be made as to whether a complete or partial sale makes sense," said a top-10 shareholder in Fresenius who declined to be named.

People close to Kriwet said on Tuesday she had planned fundamental changes to FMC's organization, while Sen wanted quick results with a view to reducing Fresenius' stake in the unit. Kriwet declined to comment.

By cutting its holding in FMC to less than 25%, Fresenius could take it off the balance sheet. The group holds only 32% in FMC, but has to fully consolidate it into its reporting due to its ownership structure.

"We would welcome a spin-off from FMC, but the question is whether it's the right time," said Florian Oberhofer, portfolio manager at Union Investment.

FMC, hit hard by U.S. staff shortages and cost inflation this year, has slashed its annual outlook twice, also pulling down Fresenius' forecasts. (Reporting by Kanjyik Ghosh in Bengaluru, Alexander Hübner in Munich and Patricia Weiss in Frankfurt; writing by Milla Nissi in Gdansk and Christoph Steitz in Frankfurt; editing by Jason Neely and Louise Heavens)