In my post "A New Monetary System From Scratch, Part 3" I concluded:
The central bank accountant follows two simple rules which he applies on a person-by-person basis: (1) if a person sells something, then credit her account, and (2) if a person buys something, then debit her account.
What is being recorded is how much each person has given or taken, without paying attention to who happened to be the counterparty in any particular trade. We know that Andy has taken goods worth SK100; from whom, it doesn't matter. We also know that Betty has given goods worth SK100; to whom, it doesn't matter. 
Before we delve further into the principles of this record-keeping system, let's assume that right after meeting Betty, Andy bumps into Carol and sells her apples priced at SK100. Following rule 1 (see quote above), the central bank credits Andy's account with SK100 and, following rule 2, debits Carol's account with SK100.
So, now we have two trades:
Trade 1: Betty gave bananas worth SK100 to Andy (without receiving anything in return)
Trade 2: Andy gave apples worth SK100 to Carol (without receiving anything in return)
The central record-keeper was duly informed, through an electronic trade reporting system (ETRS), about both of these trades and made the following entries on people's accounts (I use "T-accounts" as visual aids):
(We could close the "circle" or "triangle" by having Carol sell carrots to Betty for SK100, but I don't want to do that. In reality, we always have some open balances.)
To remind you of the purpose of this record-keeping system, here's what I said in Part 2:
Our new monetary system is about keeping records of gifts given and gifts received by each person. Betty gives a gift and this (transaction) is recorded by making a credit/positive entry – the nominal value of which reflects the value of the gift expressed in terms of the abstract unit-of-account – on her account. Andy receives a gift and this (transaction) is recorded by making a debit/negative entry on his account. Nothing moves from Andy's account to Betty's account, or vice versa. There's only a real-world 'banana flow' from Betty to Andy.
When we look at the three accounts above, we can see that Andy's overall net trade is zero (he is "even"), Betty has a credit worth SK100 and Carol has a liability worth SK100. We also know that, in keeping with the "multilateral gift economy" concept, Carol doesn't owe Betty (in particular). Carol could sell carrots to anyone and in this way get rid of her liability.
Let us now compare our system to the monetary system Nick Rowe made from scratch here (see also my Part 1).
Let's assume Nick Rowe is "airlifted" into our imaginary economy. Not being able to speak the language, Nick has to rely on his deep understanding of both trade and accounting when he tries to make sense of the exchange system.
Nick arrives just in time to witness Andy selling apples to Carol. The first thing which catches Nick's attention is that goods flow only in one direction.
"The economy might be primitive, but at least they don't rely on barter", he mumbles.
Nick also notices that the buyer of the goods, Carol, uses some kind of electronic gadget. The seller, Andy, has a gadget, too. Right after Carol has typed something in her gadget, Andy's gadget beeps. Andy looks at the screen and gives a thumbs-up to Carol. After this, they separate.
"OK. The economy cannot be that primitive", says Nick to himself. He is quite sure they are using some kind of electronic money in this economy.
Nick is thirsty and he walks into the first building that comes his way. Unfortunately, it's not a bar. It's the central bank.
Nick seems harmless enough, so the central banker lets him have a look at the electronic ledger (an unrealistic assumption, but a fairly harmless one?). There are a lot of accounts, but only three of them have had any entries made on them, and only two have open balances (see T-accounts above).
Now Nick has seen all he needed to see in order to be able to explain how the exchange system in this economy works.
First of all, we are talking about a monetary exchange economy, not unlike ours.
In Trade 1, Andy paid Betty 100 skilos for her bananas. 100 "green skilos" were transferred to Betty's account. Andy ended up having 100 "red skilos" on his account. After the trade, net money supply remained zero, while gross money supply reached 200 skilos.
In Trade 2, Andy sold apples to Carol. With the apples, Andy also delivered 100 red skilos (a medium of exchange) to Carol, thus getting rid of his liability. Now Carol is in possession of 100 red skilos.
Betty has 100 green skilos on her account and she can transfer those, as a payment, to the seller if she wants to buy some goods.
The medium of exchange, skilo, serves also as a unit of account.
[Nick continued about velocity of skilos, about IS-LM models, and so on. I left it out here because I wasn't able to follow his thought.]
Is Nick right?
 Probably I should have said "...without paying undue attention to who happened to be the counterparty...". The two entries made by the central record-keeper (central bank) do reveal the counterparty, but the point I wanted to make was that the trade doesn't establish any on-going relationship between the two parties to it. For all we know, they could be strangers to each other.