Is there any free payroll management software?

I dont think you will get a proper Payroll software for free.
The best way to run payroll more effectively and efficiently to have a company to design/customise a specific payroll software in relation to your company needs.

Easy Accounting is available online.
You can download it without any cost.

for small firm you might use excel

i have developed a softwre based on excel it does the below : calcualte the payrolll  automatically  print checks for all employees who paid by check in one click print payslips or save them or send them to employees by email automatically  give you a detailed report of types of notes of cash that you need to pay cash salalry  generate entries for all emplyees and export them to excel or pdf  calculate the basic , housing , trans and gosi salary of new employee based on the net paid decided  get a report of employees loan balances at any time get a report of employees vacation report at any time  calculate the vacation salary for any employee in one click calculate the end of service for any employee in one click get the social insurance report bsed on  cost center , project ....etc in one click get teh medical insurance report based on cost center , project ....
etc in one click get the payroll cost of each month  based on cost center , project ...
etc in one click get the provisions of vacation and end of service at any certain date  detailed or customed or by cost center or project .....
in one click save and print  the employee letters like employment sertificate , service certificate , loan certificate with the availability to add any required letter  if you are interested , just contact me through email  alahmadtamer at any of the famous mail providers like yahoo or gmail or msn  please be informed it is not for free