Round 5 - ch 3, dc in next 9 sts, skip 2 sts, ch 3, * dc in next 10 sts, sk 2 sts, ch 3* repeat from *to*  3 times, join with a sl st to top of ch 3,  Fasten off yarn.

 

Round 6 - join purple yarn in any ch 3 sp, ch 3, work 2 dcs, ch 2, 3dcs in same sp, ** ( 2 dcs in next st, 1 dc in next 2 sts) repeat sts in ( ) 3 times, 2 dcs in next st, in next corner sp work 3 dcs, ch 2, 3 dcs**repeat from **to** 3 times, ( 2 dcs in next st, 1 dc in next 2 sts) repeat sts in ( ) 3 times, 2 dcs in next st, join with a sl s to top of ch 3

 

Round 7 - ch 2, hdc in next 2 sts, * 5 hdc in next corner sp, hdc in next 20 sts* repeat from *to* 3 times, 5 hdc in next corner sp, hdc in next 17 sts, join with a sl st to top of ch 2,  Fasten off yarn

 

Note: the square will "puff" a bit in the center but will flatten out when it is joined. It also helps to pull on the corners a bit.

Chain edging for joining squares together

I am in the process of designing a chain stitch edging and will add it as soon as I am done.