Converting from one lossless format to another can be done without loss of information (that's what lossless means). Unfortunately it's slightly more complicated than thatbecause each format has different optional capabilities such as transparency and alpha. Here are some table to help you see the bigger picture:

{|class="wikitable" border="1"| From/To || BMP || GIF || PNG || JPEG|-| BMP|| Lossless || Lossless || Lossless || Loss of colour|-| GIF|| Loss of transparency flag || Lossless || Lossless || Loss of colour and transparency|-| PNG|| Loss of transparency flag || Lossless || Lossless || Loss of colour and transparency|-| JPEG || Lossless || Lossless || Lossless || Lossless|} If you have a PNG with an alpha channel: that will be lost when you convert it into any of the above. Converting from JPEG to one of the other formats is lossless, but re-encoding it as a JPEG is lossy, so converting it back to JPEGwill result in a different image than the original.