clipqgisqgis-2.18raster
Following on from Remove white background in Raster in QGIS
When I choose the unwanted value – in my case I want to remove black area around the clipped raster – I write 0 as the unwanted value, but I also lose a lot of important detail in the clipped raster. So there is a lot of differences between the original raster to the clipped raster
How can I choose to remove only the black area around the clipped raster?
Try converting your file to another/the same format (Raster/conversion/translate(convert format).There you can define a value for "no data", which you can set to a number different than 0. Hope it helps
In ArcGIS, if your output is a GRID then use the layers Symbology to not display the NoData values as shown below. 
If your output is a single band image you can set Display Background Value as 0,0,0 and as No Color but any pure back pixels will not be displayed not just the ones on the border.
Best Answer
finally, I found this solution: I put on top the layer with the desirable area i want to crop. then in the clipper function, i mark those two options:
The result will be the exact area without black areas