How long has the old antifreeze been in? What color is it? I usually don't flush the system as I do frequent cooling system maintenance. I usually just drain the system along with draining the block if I can access the plug. After old coolant is drained, I refill the system with a 50/50 mix of coolant and distilled water.
You can not add fresh coolant too slowly.......adding fresh coolant very slowly allows a little more air to "burp" out of the system.
If the cooling system has a pressure cap on the radiator, I remove the rad cap for several days (motor COLD) to check/add coolant to the proper level, as the coolant level will drop as air escapes the system. This may take several days of heat/cool cycles for the coolant level to remain at the very top of the radiator (motor COLD).
If the cooling system has a pressure cap on the bottle, watch the COLD coolant level for several days after re-filling and add coolant as needed to maintain the proper COLD coolant level.
Careful, the OP's use of the word PETROL indicates that he is not in North America. And, I KNOW that coolant 'colours' vary from those in the USA.
That said, if you DIY, just get the genuine Honda phosphated HOAT stuff from a main dealer. Factory schedules say to change it the first time at 100K miles/10 years, then every 5 years/50K miles after that. (because you don't get it all out with a drain & fill) No need to do a complete flush, as with older cars!
Here is a good description of the various types and colors of coolants (in the USA):
I should have been more specific about color.......as in if its brown, do a thorough flush before re-filling with fresh. If the color is still green, orange, yellow, turquoise, pink, blue or purple, and reasonably clean looking, a drain/re-fill should be good.