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I have for instance cash deposits that are already reconciled with invoices. How can I reconcile the general account concerned - which is not linked to a partner - from my bank statement?
In the new Bank Statement Reconciliation (V8) you have the ability to reconcile other accounts than receivable and payable ones. For those accounts you need to reconcile (without adding a partner in the bank statement), you just have to tick Allow Reconciliation for the account concerned (menu Accounting > Configuration > Accounts > Accounts).
When you encode (or import) the bank statement, leave the partner empty in the bank statement line concerned. When you click the Reconcile button, all the unreconciled entries for all accounts which allow reconciliation will be displayed (and not only payable/receivable). Then you can filter on the account code to make your searches faster. Select the counterpart to be reconciled by clicking the + in front of the line, then click OK. The entries will now be reconciled. This should solve the clearing accounts of card payments, deposits, etc.
When you return to the bank statement, you can click the Journal Items button to display all reconciliations made from this statement.
The answer given by Els Van Vossel is 100% correct
however I would like to add. A bank reconciliation consists of two columns; one for the book balance, the other for the bank balance. The person reconciling the accounts then adjusts one column by adding deposits that had not yet been recorded and subtracting checks and other outlays that had not yet been cashed when the statement had been prepared. The reconciliation is not complete until the adjusted column equals the unadjusted column. There may be some cases where the process reveals a legitimate transaction that was not recorded in the books. When that occurs, the person responsible for the business's books must record the transaction using a journal entry.