Deadlock while inserting data into a table.

I have a table X. And a trigger has been created on that table FOR Insert and update. From that trigger a stored procedure got called which insert data into another table.

Here is the insert statement :-

insert into y

select A.column1 , case y.column2 is not null then 1 else 0 end

from A

left join y

on y.column2 = A.column2

and <col1> = <col2>

So I am getting a deadlock for this insert from last few days. So is the reading data from the table and inserting the data in same table  makes some issue here?