The same

I need update a cell if a given condition is true, but I need that cell keeps its old value if the given condition is not true.
For example, try these in cell A1:

=if(C4=1,A2,A1)
=if(C4=1,A2 , )
if(C4=1,A2)

It seems ok, but now type this in cell B1 : =A1 and press enter.
Surprise!

It must be possible to leave a celle unchanged!

Please help!

Thanks

TRY THIS IN EXCEL 365 OR EXCEL 2021: since the forum system changed the equation I wrote in my original question, I'll try to explain clearly.
Cell A1 is: =if ( A2 = 1 , C4 , A1 ) In other words, cell A1 takes the value of cell C4 if A2 is 1, otherwise, if cell A2 is not 1, then cell A1 does not change, remains the same as it was.
Now put a value (33) in C4, and write a 1 in A2. Cell A1 takes the value of 33. GREAT! BUT...
Now write a 4 in cell A2, and look at cell A1. It is zero! Not the 33 it had!

My question is: how to write an IF statement where the cell changes its value if the condition is true, and the cell remains unchanged if the condition is false?
It does not work in either Excel 2021 nor Excel 365.
I had a chat with Microsoft, they told me that they do no konw the solution. WOW!!!

Thanks for your help,

Congrats, Glenn! You are an expert. I searched ITERATIVE, found the "Calculation options" and set it to Manual. IT WORKS!

One thousand thanks!!!