This page is intended to teach you how to compose a counterpoint using suspensions.  This is a complex subject but if you approach it methodically it won't be overwhelming.  In fourth species there is a given part in normal "on-the-beat" rhythmic values.  Your task is to add a counterpoint to it which essentially delays these note values by half a beat resulting in syncopations, and if you do it right, a lot of suspensions.  Example 1 shows a satisfactory fourth species counterpoint.

    The upper voice consists of quarter note values shifted to the right to create syncopations against the lower part mixed in with a few untied eighth notes which are simply 2nd species counterpoint.  Many of these syncopations are suspensions.  A suspension is a rhythmically syncopated non-chord tone that creates a dissonance on a beat which is resolved down by step after the beat.  For a suspension to be successful it must be "prepared" by a consonance.   The note on the left side of the tied note pair must be a consonant chord tone above the bass.  In the Ex. 1 the note just to the before each of the notes marked "sus" are the preparations.  The note after each suspension must be its resolution down a step.  In Ex. 1 the notes just after the notes marked "sus" are the resolutions.
    When trying to create suspensions in the higher voice part the "good" interval pairs are 4 - 3, or 7 - 6.  Rarely one will fine a 9-8 suspension in an upper part, but avoid this in your own compositions.  If you are composing a lower voice the only "good" interval pair is 2-3.
    On the other hand not every syncopated note creates a suspension, sometimes the on-the-beat portion of the syncopation will be not be dissonant but a chord tone.  In Ex. 1 the first note of bar 2 is a tied note that is simply a chord tone.  Although not as expressive as a suspension, these are fine, and since they are chord tones they do not need to resolve down by step.  A tied chord tone may be followed by a leap to another chord tone, or perhaps a passing tone.  In bar 2 beat 4 of Ex. 1 the treble "C" seems to be a suspension, but it is really a 7th of a V7 chord, so the Bb that follows is not a resolution of it, but a passing tone to the fifth of the chord, "A".

    Consider the bass line in Example 2.  We will create in a step-by-step fashion a counterpoint above it with a number of suspensions and syncopations.

    The first possible place to have a suspension is at beat 2 above the E since a suspension on the first beat could not be prepared.  So, what notes can work above the E?  Since we are composing the higher part, recall that the good suspension number pairs are 4-3 or 7-6.  In this case then we could write a 4th above E (an A), or a 7th above (D).  This calculation is easy, but the important question is "can the suspension be prepared as a consonance on the "and" of the preceding beat?"  The answer in this case is yes to both options, the 4-3 and the 7-6.  So now we simply select one of them and add its preparation and resolution.  Example 3 does just this.  The very first beat can be a half-beat rest as in Ex. 1, or you can start with a consonant chord tone and skip to the preparation of the first suspension as we see in Ex. 3.

    The rest of bar 1 we can treat in the same way, in fact on beat 4 of Example 2 the 'E' offers the same suspension possibilites as before.  So in this case we'll avoid being too repetitive by composing a 7-6 suspension on beat 4.  We can leap up to the "D" that prepares the suspension from the chord tone "A" on beat 3.  You might be inclined to tie the "G" before beat 3 across to beat 3, but this isn't the best choice as it would set up a 9-8 suspension on beat 3, a less desirable type of suspension.  Also, you should not leap up to the "D" on the "and" of beat 3 from a tied "G" because leaping from a NCT is not allowed (see Ex 4b).  As you can hear the "G" on beat 3 sounds like it needs to resolve by step, not leap up.