Is there a nontrivial oriented link with two components with linking number 0 which is related to the unknot by a single skein relation? While thinking about a problem of determining whether a given link is a slice link or not, I was lead to the following question:
Is there an oriented link with two components (other than the unlink) 


*

*whose linking number is zero

*and which, after modifying the link by applying skein relation at some place once, becomes the unknot (with a single component)?



Edit:
I found one by myself and posted it as an answer. 

I found one by myself:

Here the three tiwsts have an effect of cancelling out the -3 linking number made from the double trefoil. 
Similarly, every 2-component link with genus 1 can be realized in this way, and we can always cancel out its linking number by giving some number of additional twists. 
