That depends which currency you hold and which currency you wish to acquire, but in general, this should be possible. Consider, as an example, that an investor holds euros (EUR) and wishes to convert those to Australian dollars (AUD). This investor could purchase AUD directly with their EUR; they would not have to first sell their EUR into U.S. dollars (USD) and then use the USD to purchase AUD (although they may choose to do so).
Currency prices are most commonly quoted versus the USD in the U.S., but there are many actively traded currency pairs that do not involve the USD, and many of these exhibit very high levels of liquidity. For example, the euro/British pound (EUR/GBP), euro/Swiss franc (EUR/CHF), and Australian dollar/Japanese yen (AUD/JPY) are all highly liquid currency pairs, to name but a few.
Generally speaking, the G10 currencies are very liquid and readily convertible from one to another. Some, less frequently traded currency pairs may exhibit lower liquidity and hence larger spreads and therefore transaction costs. The decision whether to convert directly, or to first sell into USD, then use the USD to purchase the desired currency, is largely dependent upon the level of liquidity the currency pair exhibits.
An exception to this is when a currency is non-convertible, such as the Chinese yuan (CNY). In a future Currency Corner we will discuss non-convertible currencies in more detail.