Wepresentasufficientandnecessaryconditionforaso-calledCnkpatterntohavepositivesemidefnite(PSD)completion.SincethegraphoftheCnkpatterniscomposedbysomesimplecycles,ourresultsextendthosegivenin[1]forasimplecycle.WealsoderivesomeresultsforapartialToeplitzPSDmatrixspecifyingtheCnkpatterntohavePSDcompletionandToeplitzPSDcompletion.