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We propose a new scheme of serially concatenated continuous phase modulation (SCCPM) by using nonsystematic low density generator matrix (LDGM) codes as the outer code. We use the EXIT chart/function to optimize the LDGM codes. We also show the EXIT function for CPM when the SNR (signal-to-noise-ratio) is fixed. A property of the LDGM code degree is investigated. The union bound is used to analyze the error floor. Numerical results show that this scheme converges earlier (lower SNR) than previous considered SCCPM schemes for iterative decoding.