If your CPU's chipset is not supported by your motherboard's chipset, then they are not compatible.
This means if your motherboard only supports the Intel 845 chipset, and you get a CPU that needs only the 855 chipset, then they will not work!
Sometimes updating the BIOS will enable the motherboard to support more modern processors, but not all the time, since the hardware (the chipset) influences more on which CPUs it can support.
A more effective way of answering your question even further would be possible if you tell us the name of the motherboard and the exact model of your Pentium M. Links would help with this.