In my experience, negativity is often a symptom. Rather than treat the symptoms, the negativity being expressed, it is better to search out the crux of the problem.
Perhaps it is an individual, a ‘negative’ leadership personality, in which coaching and/or other change may be required.
More often, I find negativity stems from senior management, from the ‘leadership.’ This comes in the form of unstated expectations; no clear direction and/or strategy for the company and/or its business units; frequent changing of direction (see prior); and, first and foremost–poor communication.
Whatever the cause, until you seek it out and begin to address it (ideally transparently), the symptoms will persist.