Is it a negative sign for a company when it reduces its dividends, even when it is still relatively high/good dividends compared to others?
A reduction in the dividend may signal a change in the profitability of the company. Dividends are supposed to come from retained earnings, and if the forecast by the company shows that they can't continue to afford to pay their current dividends, the reduction of the dividend amount could be the first sign of problems.
To be fair, it could also mean that they want to use the money they are spending on dividends on an expansion of the business by acquiring another company or expanding capacity.
The company announcements should contain information regarding the reasoning behind the decision.
Reducing the dividend will upset the portion of stockholders that consider the dividend the most important reason for continuing to own their shares.