This link shows it better (link to tx vs the address).
https://blockchain.info/tx/f045f489dd97e8a66e4551d67b117678a558a068ce886cba1aa47b6f7eee84f0That wasn't a fee. It was change. Bitcoin can't spend part of output so it needs to make change
The person making the tx had outputs worth: 0.11097293 BTC and wanted to spend 0.1 BTC.
For some asinine reason they decided they wanted to include a single satoshi (0.0000001 BTC) as a fee (not exactly sure why).
Inputs must equal outputs + fee.
However the user didn't want to spend 0.11097292 BTC they wanted to spend 0.1 BTC so the client made a tx like this
IN0: 0.02465968 BTC
IN1: 0.08631325 BTC
OUT0: 0.1 BTC <---- amount user wanted to spend
OUT1: 0.01097292 <---- the "change" sent to another address controlled by the user.
FEE: 0.00000001 BTC
You will notice the sum of the inputs minus the sum of the outputs is 0.00000001 BTC which is the fee paid to the miner.
Think of it like you want to buy a candy bar for $1 but you only have a single $20 bill. How large will the tx be. Well it can't be $1 because you don't have $1. The tx will be $20. So you send $20 to the cashier and she sends back $19 in change and puts $1 into the store's account.
In Bitcoin terms it would be like this:
IN0: $20.00 <- your single $20 bill
OUT0: $1.00 <- your payment to merchant
OUT1: $10.00 <- your change in the form of $10 bill, $5 bill and 4x $1 bills
OUT2: $5.00
OUT3: $1.00
OUT4: $1.00
OUT5: $1.00
OUT6: $1.00
FEE: $0.00
You will notice the merchant had to give you a large number of discrete outputs (smaller bills). This is because in fiat currencies the currency can only exist is predefined forms ($1, $5, $20, $100, etc). Bitcoin however can create a new output of any value thus in the Candy bar analogy it would be like "You hand cashier a $20 bill, she securely destroys it and prints a new $1 bill and $19 bill, she puts the $1 in the teller and hands the $19 bill back to you".
